I was considering a feat called Outside Training.  The idea of the feat would be that it can let you learn a single feature from another class or archetype.  This can not be a feature that would be covered by any other feat, nor can it require any prerequisites you do not have (such as taking a level 7 feature when you are level 4).

Does this sound useful without being overpowered?

It sounds overpowered, depending on the features you allow it to provide. 

Like everyone having Action Surge without needing to take Fighter dips? Nah.

Everyone getting infinite casting of a 1st or 2nd level spell, without being a Wizard?

Everyone getting Portent?

And so on.

Nah. Little things like Metamagic Adept, etc are fine but the feat, as you described it, is beyond.

Well obviously not infinite casting of a first or second level spell, I do not think even Wizards get that.  Portant is not unreasonable, since it can only be used twice a day.   Action surge, as it requires a rest before trying it again, might not be unreasonable either.  Still, that is why I am asking opinions.  It may be too powerful, what would be a suggested re-write?

An alternate suggestion would be a Retraining feat if someone decides they do not like their current Archetype and decides to change it.  As far as I can see, the normal rules do not cover that possibility.

Or, possibly, to exchange a class feature for an equivalent class feature?

Quote from AlanGunhouse >>

Well obviously not infinite casting of a first or second level spell, I do not think even Wizards get that.  

They do. Spell Mastery feature. You pick a 1st level and 2nd level spell. While prepared you can cast those spells without using spell slots as much as you want. With 8 hours of study you can change which spells to use for the feature.

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Anyway, major key features like Portent and Action Surge are powerful. Acquisition of these without class dips is way, way too strong. So you would need to be very careful about what features can be granted : and that's an exhausting enterprise.

Being able to change your subclass whenever you want, even once per day, is also rather strong. That's an entire party able to rewrite their core builds as needed for any mission. That will, most assuredly, strain the DM's patience considerably because now, no matter what mission, the party can just instantly optimise for it. It also wouldn't make sense. How does a Dragon Sorcerer become a Clockwork Sorcerer? Or a Fiend Patron warlock become an Archfey Patron Warlock? This has nothing to do with training. 

Game balance is a tricky thing when homebrewing. 

The intention of your feat (which, remember, a variant human or custom lineage could start the game with) is very much "I want all of X class features and Y subclass features PLUS Z class/subclass feature for basically no real cost!!" and it's just a bit much. 

Exchanging a subclass feature for a different subclass feature that is equal or lower level from the same class - would be a good deal. 

The intent is "I want JUST ONE of the features of another class"...and it is not intended to be changed.  
That said, If exchanging a feature seems more reasonable, it is worth thinking about...

If you restricted it to only 1st level features and only from base classes (not subclasses), and if you put a prerequisite of 4th level on the feat then it would probably be mostly okay. Probably. Mostly.

I would not create such a feat for the express reason that I am not clever enough to anticipate and try to mitigate the unintended game-breaking consequences. I would be interested in a few well-crafted feats in the style of metamagic adept that are specific.

Quote from AlanGunhouse >>

The intent is "I want JUST ONE of the features of another class"...and it is not intended to be changed.  
That said, If exchanging a feature seems more reasonable, it is worth thinking about...

 

 Even just exchanging a feature is extremely easily broken. Here's what I came up with as broken combos after thinking about it for just a few minutes:

1) Fighter + Rage - getting that +2 damage to all attacks and resistance to physical damage is super powerful.
2) Twilight Cleric + Shadow Step (Shadow Monk) - you're CD produces dim light around you all the time, and you can use the Adv for an Inflict Wounds for huge damage.
3) Taking Action Surge on any caster.
4) Taking Cunning Action on any caster -> now you can cast a spell then Hide every round.
5) Evasion... on everyone - Geez, who wouldn't take Evasion if they could?
6) Aura of Protection.. on every CHA-caster -> if you've got a good CHA why wouldn't you take Aura of Protection?
7) Bladesinger's Extra Attack.. on all the melee-clerics, and rogues, and bards, and druids,....
8) Dragon Sorcerer's Dragon Wings.. on everyone
9) Hexblade's Curse .. on every Barbarian and Rogue and Fighter and Monk
10) Bardic Inspiration on every CHA-caster
11) Wild Shape.. on every sneaky character
...
...

Which is why my suggestion was the exchange was in the same class and between subclass features that were equal level (the new one being lower than your current one). Like A Conjuration Wizard  swapping Benign Transposition with Sculpt Spells. 

Quote from Cyb3rM1nd >>

Which is why my suggestion was the exchange was in the same class and between subclass features that were equal level (the new one being lower than your current one). Like A Conjuration Wizard  swapping Benign Transposition with Sculpt Spells. 

 Doesn't really fix it though. Bard gets "Countercharm" at 6th level so could swap it under your suggestion for "Aura of Protection" which would be pretty bonkers as a build. Warlock depends how you count stuff, is getting a new Invocation getting a new class feature? if so they can pick up Aura of Protection at 7th level. 

Rogues can swap one of their 3rd level subclass features (many of which aren't very powerful) for Hexblade's Curse. Swap Uncanny Dodge for Extra Attack, or since their 9th level subclass features mostly suck so they could easily use one of those for Battlemaster Maneuvers, or Gloomstalker's Dread Ambusher, or Extra Attack from Bladesinger or Valor Bard.

Ranger can swap Primeval Awareness (have you ever seen this used?) for Wildshape or Cunning Action, or Action Surge.

Druid could swap Wildshape for Action Surge, Cleric can swap Turn Undead for Action Surge, Bard can swap Jack of All Trades for Action Surge (or any of them could swap instead for Cunning Action).

Paladins could swap Divine Sense (have you ever used this?) for Bardic Inspiration, Hexblade's Curse, or Rage

Fighters could swap their Fighting Style for Rage.

Barbarian could swap Brutal Critical for Evasion or Stillness of Mind. 

Quote from Agilemind >>

Quote from Cyb3rM1nd >>

Which is why my suggestion was the exchange was in the same class and between subclass features that were equal level (the new one being lower than your current one). Like A Conjuration Wizard  swapping Benign Transposition with Sculpt Spells. 

 Doesn't really fix it though. Bard gets "Countercharm" at 6th level so could swap it under your suggestion for "Aura of Protection" which would be pretty bonkers as a build. Warlock depends how you count stuff, is getting a new Invocation getting a new class feature? if so they can pick up Aura of Protection at 7th level. 

Rogues can swap one of their 3rd level subclass features (many of which aren't very powerful) for Hexblade's Curse. Swap Uncanny Dodge for Extra Attack, or since their 9th level subclass features mostly suck so they could easily use one of those for Battlemaster Maneuvers, or Gloomstalker's Dread Ambusher, or Extra Attack from Bladesinger or Valor Bard.

Ranger can swap Primeval Awareness (have you ever seen this used?) for Wildshape or Cunning Action, or Action Surge.

Druid could swap Wildshape for Action Surge, Cleric can swap Turn Undead for Action Surge, Bard can swap Jack of All Trades for Action Surge (or any of them could swap instead for Cunning Action).

Paladins could swap Divine Sense (have you ever used this?) for Bardic Inspiration, Hexblade's Curse, or Rage

Fighters could swap their Fighting Style for Rage.

Barbarian could swap Brutal Critical for Evasion or Stillness of Mind. 

 
I've already said it twice so please forgive my sass here but..

 Since ya missed is twice I'mma highlight it a bit more. A smidge....

Quote from Cyb3rM1nd >>

Which is why my suggestion was the exchange was in the same class and between subclass features that were equal level (the new one being lower than your current one). Like A Conjuration Wizard  swapping Benign Transposition with Sculpt Spells.