Taking some of the ideas from other threads, and updating a previous set of thoughts I had, I though tI would post my current thoughts.

The underlying mindset of this is: bringing back some of the Monk capabilities of earlier editions, and especially the ubiquity of Martial Arts in the 1e OA book (able to be learned by any class), but using 5e/OneD&D mechanics to do it.  So this is NOT JUST a Monk thread, but also a thread for any unarmed fighting character, including a way to do a Mundane (non-mystical) Martial Artist via Weapon Mastery and Battle Master, that also integrates with the Monk and Sword Bard.

Feat: Fighting Style: Unarmed
Prerequisite: Warrior Group, Expert Group, and/or Fighting Style feature

• You have a Martial Arts Die of 1d6
• Damage for your Unarmed Strikes = Martial Arts Die + Ability Modifier
• Your Unarmed Strikes are considered to be Finesse weapons (including for all features, feats, and spells that reference a weapon, including spells that might otherwise have a specific weapon requirement or weapon value requirement).
• Your Unarmed Strikes also have the Light property.  Each appendage you have that can make attacks or wield weapons (when not wielding a weapon nor shield), and not holding any other object, counts as a "different light weapon" for the Light weapon extra attack. Unlike other Light weapons you DO retain your Attribute Bonus to damage for this extra Unarmed Strike attack if it hits.
• If you learn a Weapon Mastery, you may learn it for your Unarmed Strikes.  The Mastery property for Unarmed Strikes is Nick.  You may also learn other Weapon Masteries for your Unarmed Strikes if they would work with Finesse and/or Light weapons.

Fighting Style: Defense

• Change: Prerequisite: Warrior Group and/or Fighting Style feature
• Change: The AC bonus applies without regard to armor worn.

Feat: Martial Adept
(if you have Bardic Inspiration Dice, Discipline Points, or Superiority Dice, then you may use those features to empower the maneuvers learned through this Feat, but the Superiority Dice you gain through this feat do not sale up, and remain d6's)

Feat: Martial Arts Expert
Prerequisite: 4th Level, Fighting Style: Unarmed
Repeatable: No.

• If you know or prepare any spell that can be use on or with a weapon that you wield, you may use it to enhance your Unarmed Strikes.
• You gain 2 Discipline Points (DP) (or 2 more if you already have them).  You regain any spent Discipline Points when you complete a Short Rest or Long Rest.
• As a Bonus Action, you may spend 1 DP to add a magical +1 to your attack and damage rolls with Unarmed Strikes, and also to your Armor Class  This lasts for 1 minute.
• When you deal damage with an Unarmed Strike, you may spend 1 DP to add another roll of your Martial Arts Die to the damage.

Battle Master Maneuvers (expansion to the existing list of maneuvers):

• Throw: When you make an Unarmed Attack, and hit, you may expend a Superiority Die to force the target to make a Dexterity saving throw or be knocked prone.  If they fail the saving throw, add the roll of your Superiority Die to the damage you inflict.
• Lock: When you successfully Grapple a target, you may expend a Superiority Die and add it to your Grapple check.  If you succeed, they are unable to attack any target other than you, and they are at disadvantage to attack you.
• Retreat: You may use a Superiority Die to use the Disengage action as a Bonus Action.  Roll the Superiority Die and add it to your movement for the rest of this turn.
• Choke: If you have successfully Grappled a target, you may spend a Superiority Die to force it to make a Constitution save or become unconscious for half as many rounds as you roll on that Superiority Die.
• Reversal: If a creature successfully Grapples you, you may use a Superiority Die to add to your Grapple check.  If your roll succeeds, you have not only avoided their Grapple, but you may choose to Grappled them instead, and may apply the Grappled condition to them instead of you.
• Prone Fighting: If you are prone, but not Grapples, Incapacitated, Restrained, nor Unconscious, you may spend a Superiority Die to remove the prone condition without expending any movement.  While Prone, your unarmed strikes do not have disadvantage.  Attack rolls made against you while Prone do not have advantage simply because you are Prone.
• Immovable: If you are Grappled, and the creature Grappling you tries to move you, you may expend a Superiority Die to reduce the movement they are trying to use to move you this turn.  You reduce the movement by 3x the amount you roll on the Superiority Die.
• Leap: when you try to Jump, you can use a Superiority Die to either add to your Attribute Check for the Leap, or to extend the distance of the Jump.
• Flurry of Blows: You can expend a Superiority Die to use a Bonus Action to make an Unarmed Strike.  Before you make the attack, roll the Superiority die.  You may add some or all of the roll to the attack roll, and the rest to the damage if the attack hits.  You may allocate how much (if any) of the roll to the attack after you roll the attack but before you know whether or not it hits.
• Centering: You may expend a Superiority die to grant you two temporary Discipline Points.  You lose all temporary Discipline Points when you complete a short rest or long rest.
• Pugilist: When you make unarmed strikes, you may use your Superiority Die type as your Martial Arts Die type.
• Defensive Stance: When someone makes an attack roll against you, after you know the total but before the attack is resolved, you may use your Reaction to expend a Superiority Die and add half the roll (round fractions up) to your AC until the start of your next turn.  This AC Bonus does not stack with AC Bonuses from any other Battle Master Maneuver.
• (3 Maneuvers that replace the Bardic Flourishes from the College of Swords) (use a Superiority die instead of a Bardic Inspiration die) (each one can only be used once per turn)
• (You can use Maneuvering Attack on yourself)

Background:   Temple of the Crimson Mountain
The Temple of the Crimson Mountain (and other temples like it) is a secluded monastic temple that specializes in the lessons and teachings of channeling mystical energies through your body.  This includes Spell Casters, Monks, and some others.  (you may wish to consider the power level of this Background, as its Bonus Spells puts it on par with Strixhaven backgrounds)
Attributes:  +2 DEX, +1 (pick WIS, CHA, or INT)
Languages: pick one
Skill Proficiencies: Pick two from: Athletics, Acrobatics, Medicine, Religion
Tool Proficiencies: pick one Musical Instrument
Feat: pick one from: Fighting Style: Unarmed or Magic Initiate (any)
Bonus Spells:
You always have these spells prepared, once you are of the listed character level or higher, even if you don't have spell slots with which to cast them.  They do not count against your number of spells known/prepared from any of your classes.  If you have Bardic Inspiration Dice, Discipline Points or Superiority Dice, you may use a Bardic Inspiration Die or Superiority Die to cast one of the 1st level spells, or (1 + Spell Level) in Discipline Points to cast any of these spells, without expending a Spell Slot.  You may also cast them with Spell Slots if they are of the appropriate level.

• 1st Character Level: Jump, Shield of Faith
• 3rd Character Level: Levitate, Pass Without Trace
• 5th Character Level: Water Breathing, Water Walk
• 7th Character Level: Freedom of Movement, Stoneskin
• 9th Character Level: Commune with Nature, Tree Stride

Note about Bardic Inspiration Dice, Martial Arts Dice, and Battle Master Superiority Dice (those acquired directly through the Battle Master subclass, not through other sources):  They should all scale up at the same rate/time instead of Bard and Monk having different progressions and the Battle Master's not increasing at all.

Barbarian:
You may choose to replace one of your 1st level Weapon Masteries with a Fighting Style, including Fighting Style Unarmed.  This also qualifies you for taking Fighting Style feats whether you take one now or later.

Bard: College of Swords

• Your Fighting Style choices include "Fighting Style: Unarmed".
• Your Bardic Inspiration Dice should increase at the same rate as the Monk's Martial Arts Dice (or visa versa),
• Replace the Bardic Flourishes with learning 3 Battle Master Maneuvers that are powered by your Bardic Inspiration dice (and/or any Superiority dice you might have).

Cleric:
Divine Order: Protection Order may choose Fighting Style: Unarmed instead of the Martial Weapon Proficiency and Heavy Armor training.

Druid:

• While in Wild Shape, a Druid explicitly retains any Monk features they may have, unarmed strike features/abilities/maneuvers, and may chose the unarmed damage they normally can do, or that their Wild Shape natural attacks/claws/etc. can do, whichever is higher.

Fighter:

• The mundane martial artist build is:
• 1st Level:
• Fighting Style: Unarmed
• Weapon Mastery: One of your picks should be: Unarmed Strikes (Nick)
• 3rd Level: Battle Master (keeping in mind that Unarmed Strikes are considered to be Light/Finesse weapons, and thus work with Battle Master Maneuvers that work with a weapon that the character is wielding) -- Good idea to take "Pugilist" and "Flurry of Blows".
• 4th Level: Feat: Martial Arts Expert
• 6th Level: Feat: Defensive Duelist
• Semi-Mundane martial artist build:
• 1st Level:
• Fighting Style: Unarmed
• Weapon Mastery: One of your picks should be: Unarmed Strikes (Nick)
• 3rd Level: Eldritch Knight
• 4th Level: Feat: Martial Arts Expert
• 6th Level: Feat: Martial Adept (Pugilist, Flurry of Blows)
• Battle Master Dice: start as d6's and increase in size at the same rate as the Monk's martial arts die.  This includes dice obtained through the Martial Adept feat.

Monk:

• Replace "Dexterous Attacks" and "Bonus Unarmed Strike" with "Fighting Style: Unarmed"
  This DOES qualify you for other "Fighting Style" Feats.
  (don't fret about losing the Bonus Unarmed Strike, your Unarmed Strikes will count as a Light weapon but WITH the Attribute bonus damage)
• Optional Rule (replaces Wisdom as a requirement for Monk abilities, Save DC's, Unarmored Defense, etc.):
  Monastic Discipline -- You learned a form of Martial Art that channels some other form of energy though your body, fueling your Martial Arts and Mystical Abilities.  Pick one of the three fundamental disciplines of your Monastic Order:
• Mind over Matter: Your discipline is based upon channeling psionic energy into unarmed combat.  You use Intelligence as your Mystical Attribute (replaces Wisdom for your DC calculations for your special abilities, Unarmored Defense, etc.).  When you gain the Empowered Strikes feature, with each individual attack, you may choose to do Psychic damage as your Unarmed Strike damage type.
• Spirit over Matter: Your discipline is based upon channeling spiritual energy into unarmed combat.  You use Wisdom as your Mystical Attribute (DC calculations for your special abilities, Unarmored Defense, etc).  When you gain the Empowered Strikes feature, with each individual attack, you may choose to do Radiant damage or Necrotic damage (pick when you gain this feature) as your Unarmed Strike damage type.
• Vitality over Matter: Your discipline is based upon channeling vital energy into unarmed combat.  You use Constitution as your Mystical Attribute (replaces Wisdom for your DC calculations for your special abilities, Unarmored Defense, etc).  When you gain the Empowered Strikes feature, with each individual attack, you may choose to do Poison damage as your Unarmed Strike damage type.
• Mystical Fighting: You may replace Strength and/or Dexterity with your Mystical Attribute (or Wisdom if not using that optional rule) as the Attribute Modifier for your Attack and Damage rolls with Unarmed Strikes, Simple Weapons that don't have the Two Handed property, and Chosen Weapons from the Warrior of Weapons subclass.
• Weapon Mastery (change to the existing feature): You learn the Mastery Property for your Unarmed Strikes (Nick), and may learn one more Mastery property that you can use with your Unarmed Strikes.  Only one of these properties can be active at any given time, and you change which one you are using when you complete a Short Rest or Long Rest.
• Martial Discipline (addition to existing feature): Add the greater of your Proficiency Bonus or your Wisdom Modifier (or your Mystical Attribute bonus if you're using that optional rule) to your number of Discipline Points.
• Replace "Flurry of Blows" with:
• You learn 2 Battle Master Maneuvers.  Instead of activating Battle Master Maneuvers with Superiority Dice, you may spend 2 Discipline Points (you may also use Superiority Dice if you have them).  When you do so, if the Maneuver (including Maneuvers learned through the Martial Adept Feat) calls for you to roll a Superiority Die, you may roll a Martial Arts Die instead.  If it requires a saving throw, the DC is the same as your Martial Discipline Save DC.  You learn 1 more Maneuver of your choice at 7th level, 10th, and 15th levels.  Each time you learn new maneuvers you may replace one (all?) you know with a different one.
• (note that Flurry of Blows is now a slightly different Battle Master Maneuver, so you can still choose to pick that up, and when combined with the Nick weapon mastery will still get you the same number of Unarmed Attacks per round; the downside is that it basically costs 2 DP instead of 1 ... which has been compensated with more DP and the extra attack/damage effect for the Maneuver)
• Replace "Patient Defense" with "Deflect Attacks" (the first paragraph of "Deflect Missiles", but you can use it against melee weapons, unarmed strikes, or ranged weapons).
• If you're concerned about losing "Patient Defense", consider the "Defensive Stance" Battle Master Maneuver as your second maneuver gained at 2nd level.
• Replace "Deflect Missiles" with "Redirect Attacks" (the second paragraph of "Deflect Missiles", but you can use it against melee weapons, unarmed strikes, or ranged weapons).
• Replace "Empowered Strikes" with:
• At 6th level, you gain a magical +1 to Attack and Damage rolls with Unarmed Strikes and Unarmored Defense.  You may also substitute your damage type with Unarmed Attacks with Force, or the damage type from "Monastic Discipline" (if you're using that optional rule).
• At 13th level, the bonus increases to +2.
• These bonuses DO stack with Martial Arts Expert.
• At 9th Level, as part of "Acrobatic Movement", you may now use a Bonus Action to use Disengage OR Dash (but not both) without spending a DP.
• At 10th Level, you learn a third "Weapon Mastery" property that you may use with your Unarmed Strikes.
• At 15th Level, In addition to "Perfect Discipline", you gain the Weapon Adept feature from the Fighter.

Monk Subclass: Warrior of Weapons (replaces the Way of the Kensei subclass)

• 3rd Level
• Disciplined Weapons: You gain proficiency with Martial Weapons.
• Chosen Weapons:
• You pick one melee weapon and one ranged weapon.  You must already be proficient with these weapons, and they may not have the Heavy property.  You may pick another Chosen Weapon each time you gain a subclass feature (at 6th level, 11th level, and 17th level), as long as you are already proficient with that weapon (these 3 additional Chosen Weapons do not have any restriction about being heavy nor two handed).
• Each time you attack with a Chosen Weapon, you may chose to use the weapon's defined damage dice, or to substitute your Martial Arts Die instead.  You may also choose to use your Mystical Attribute's modifier for the attack and damage rolls to replace Dexterity and/or Strength.
• If any of your Chosen Weapons have the Thrown property, you may use a Bonus Action  to bestow the "Returning" property to some or all them (your choice).  They must be in your possession (in your carried equipment, in your hand, etc.) when you do this.  It costs 1 Discipline Point per weapon to do this, and lasts for 10 minutes.
• Weapon Mastery:
• You learn the Weapon Mastery features of both of your Chosen Weapons.  Each time you gain a new Subclass feature (at 6th level, 11th level, and 17th level), you learn the Mastery type for your new Chosen Weapon gained at that level.
• 6th Level
• Energetic Blade: Your “Empowered Strikes” Monk class feature also applies to your Chosen Weapons.  Any of the energy damage types that you can do with your Unarmed Strikes via Empowered Strikes (not including Bludgeoning, Piercing, or Slashing) can be used as a substitute for the damage type of your Chosen Weapon, chosen for each attack separately.  If the Chosen Weapon you're wielding is not magical already, then the bonus you gain from Empowered Strikes also applies to your Chosen Weapon.
• 11th Level
• Battle Master Maneuver: If you do not know the "Flurry of Blows" maneuver, you learn it now.  If you already knew it, you learn another Battle Master Maneuver.
• Flurry of Blades: You may use the “Flurry of Blows” feature with your Chosen Weapons, making one or both attacks with a Chosen Weapons instead of an Unarmed Strike.
• 17th Level
• Disciplined Aim: Once per turn, if you miss with an attack roll using a Simple Weapon or Chosen Weapon, you may re-roll the attack roll.

Monk Subclass: Warrior of Mysticism

• 3rd Level
• Spellcasting:  You may learn spells using the same progression and number of spells known as the Arcane Trickster.  When you gain this feature, you must choose one of the 3 main spell lists (Arcane, Divine, or Primal) as your spell list.  At all times, half of the Leveled Spells you know (rounded up) must have a range of Touch or Self, or be related to the energy type that is related to your Monastic Discipline feature (starting at 6th level, they also may be related to an energy type that is compatible with your Empowered Strikes feature).  Leveled Spells you learn via Martial Arts Mastery, and the extra Leveled Spell you learn at 11th level, count toward satisfying this fraction.  Your Spellcasting Ability is determined by the Mystical Attribute from your Monastic Discipline feature (or Wisdom if you're not using that optional rule).  Unlike the Arcane Trickster, you do not have to use one of your cantrips known to learn Mage Hand, and you are not limited to the Enchantment nor Illusion schools of magic for 2 of your spell picks.  You otherwise use and are bound by the rules for the Arcane Trickster's 3rd level Spellcasting feature (this DOES NOT include "Mage Hand Legerdemain" nor any of the higher level Subclass features for the Arcane Trickster).
• Martial Focus: You may use a Simple Weapon, except those that have the Two Handed property, as a spellcasting focus.
• Font of Discipline: If you have Sorcery Points as well as Discipline Points, you may use a bonus action to convert Spell Points to Discipline Points, or visa versa.  You may never have more than your normal maximum of either type of points.
• 6th Level
• Cantrip Attack: When you take the Attack Action, you may use one (and only one) of your Attack Action attacks to cast a cantrip that you know.
• Metamagic: You learn one Sorcerous Metamagic option.  You may directly use Discipline Points (or Sorcery Points) to activate this option.
• Bonus Cantrip: You learn one new Cantrip, increasing the number of Cantrips you know.  It can be from any of the Arcane, Divine, or Primal spell lists.  It must be a Cantrip that has a range of Touch or Self, or it must be related to an energy type that is compatible with your Empowered Strikes feature.
• 11th Level
• Metamagic: You learn one Sorcerous Metamagic option.  You may directly use Discipline Points (or Sorcery Points) to activate this option.
• Bonus Spell: You learn one leveled spell that doesn't count against your limitation of spells known/prepared.  It can be from any of the Arcane, Divine, or Primal spells.  It must be a 1st or 2nd level spell.  It must be a spell that has a range of Touch or Self, or it must be releated to an energy type that is compatible with your Empowered Strikes feature.
• 17th Level
• Spell Strike: Once per turn, when you hit with an unarmed strike, you may use your Bonus Action to immediately cast a spell you know, that has a casting time of Action or Bonus Action, and that can only affect one target.  That target must be the target of your unarmed strike.

Paladin:
You may pick Unarmed as your 2nd level fighting style.

Ranger:
You may pick Unarmed as your 2nd level fighting style.

Rogue:

• Replace your Tool Selection with:  Thieves Tools OR one artisan tool or musical instrument of your choice.
• Replace Thieves Cant with: a bonus 1st level Feat (not ASI), which can include Fighting Style: Unarmed.
• The mastery property for Psychic Blades is Nick, and Psychic Blades always appear when you have the ability to make an attack.

Sorcerer Subclass: Physical Sorcery

• 3rd Level
• Fighting Style: Unarmed
• Monastic Discipline -- Magic Over Matter: You channel your knowledge of Magic and the Weave into your unarmed strikes.  You use Charisma as your Mystical Attribute for any Martial Arts Masteries, your Unarmed Defense modifier, and the option to use your Charisma Modifier as the attack and damage modifier for your unarmed strikes.  When you gain this feature, you also pick one type of damage to also use as an option for the Empowered Strikes feature when you gain it:  Psychic, Radiant, Necrotic or Poison.
• Martial Focus: You may also use a Simple Weapon, except those that have the Two Handed property, as a spellcasting focus.
• Unarmored Defense: You gain the "Unarmored Defense" feature (the same as the Monk class feature of the same name, using your Charisma Modifier as your mystical ability).
• 6th Level
• Bonus Unarmed Strike: When you use the Magic Action, you may use a Bonus Action to make an Unarmed Strike.
• Font of Discipline: You may use a bonus action to convert Spell Points to Discipline Points, or visa versa.  You may never have more than your normal maximum of either type of points.  You may use your Sorcery Points as a substitute for the requirement of Discipline Points when learning Martial Arts Masteries.
• 10th Level
• Empowered Strikes: You gain the Empowered Strikes feature (the same as the Monk class feature of the same name).  You may apply the bonus from Empowered Strikes to melee spell attacks that you might make.
• Bonus Cantrip: You learn one new Cantrip, increasing the number of Cantrips you know.  It can be from any of the Arcane, Divine, or Primal spell lists.  It must be a Cantrip that has a range of Touch or Self, or it must be related to an energy type that is compatible with your Empowered Strikes feature.
• 14th Level
• Spell Strike: Once per turn, when you hit with an unarmed strike, you may use your Bonus Action to immediately cast a spell you know, that has a casting time of Action, and that can only affect one target.  That target must be the target of your unarmed strike.
• Bonus Spell: You learn one leveled spell that doesn't count against your limitation of spells known/prepared.  It can be from any of the Arcane, Divine, or Primal spells.  It must be a 1st or 2nd level spell.  It must be a spell that has a range of Touch or Self, or it must be releated to an energy type that is compatible with your Empowered Strikes feature.

Warlock:
Pact of the Fist: (instead of a bonus cantrip, you get FS: Unarmed, and you may use Legacy of the Ancients to pick up Martial Arts Expert when you are 4th level or higher)(Eldritch Invocations that require Pact of the Blade may instead be used with Pact of the Fist as a substitute requirement, but they may only be used with your unarmed strikes)

Wizard: Bladesinger
You may choose Fighting Style: Unarmed instead of the Martial Weapon Proficiency and Armor training you usually gain as a Bladesinger.  If so, you may use your Intelligence modifier (instead of Strength or Dexterity) for your Attack and Damage rolls for Unarmed Strikes.

Based on something I saw elsewhere (from Haravikk), I'm making the following changes:

Battle Master Maneuvers (delete "Retreat" and "Defensive Stance", reword Flurry of Blows, and add these other two)

• Step of the Wind:  You may use a Bonus Action to Disengage.  When you do this, you may also choose to expend a Superiority Die, double the result, and add that to your movement.
• Flurry of Blows:  You may expend a Bonus Action to make an Unarmed Strike.  When you do this, you may also choose to expend a Superiority Die: After you roll the Bonus Action attack, but before you know whether or not it hit, you may add some, none, or all of the die roll to increase your attack roll.  Any amount you do not add to the attack roll may instead be added to the damage the attack inflicts if it hits.
• Patient Defense: During your turn, you may expend a Superiority Die to Dodge without consuming an Action.  Roll the Superiority Die, and you may use your Reaction to apply half of the roll (round fractions up) to increase your AC against one attack made against you before the start of your next turn.

The point being: for Step of the Wind and Flurry of Blows, you can get a basic benefit from just giving up your Bonus Action, and then enhance that if you ALSO expend a Superiority Die / 2 DP.   Where with Patient Defense, you definitely have to consume a Superiority Die (making this less attractive as a 2 level Monk dip, because you would only be able to do this once per short/long rest), and can expend your Reaction to further gain benefit from that Superiority Die.

Remove the 9th level monk bullet item:

• At 9th Level, as part of "Acrobatic Movement", you may now use a Bonus Action to use Disengage OR Dash (but not both) without spending a DP.

Instead, add to "Heightened Metabolism" at 7th Level:  In addition, you may use the Dash action as a Bonus Action.

So, you get most of the benefit of the old "Step of the Wind" via the Battle Master Maneuver, but if you want to just Dash without expending a Superiority Die, that's part of your heightened metabolism now.

It may also be worth renaming "Battle Master Maneuvers" to "Martial Maneuvers" ... where the Battle Master happens to get a lot of them, the Monk gets many of them, and "Martial Adept" gets you two of them.