Obviously it is MAD to a high degree requiring maxing Dex, Wis, and Int And still needing decent Con .
The big advantages are:
the Song of victory specifies "Starting at 14th level, you add your Intelligence modifier (minimum of +1) to the damage of your melee weapon attacks while your Bladesong is active."
That seems pretty clear then that you could use them together. It isn't broke or anything, however it does mean that a monk could be doing 1d8+10 for each of 2 regular attacks and 1d6 +10 for each flurry of blows.average of 56 damage (assuming all hit) with 1 ki point. And that isn't including Haste as an option or a Shadow blade (see below).
The AC potential here is interesting, with the possibility of a 27 while bladesinging and with the +2 Agile Parry bonus. 29 if you have bracers of d. If you wanted to go full on AC crazy you could use all 3 attunement slots for a bracers, a ring of protection, and a cloak of protection and get to 31. If hasted 33.
Shadow blade is an interesting question here: could it be a monk weapon? It seems to fit the requirements. Since you don't get the regular spell progression this spell becomes worth casting at high levels because that is upping the 2 regular attacks to 5d8+10 each, per round you can keep concentration. 10d8+20, +2d6+20 per round as long as slots and concentration and ki hold up. If someone else can haste you, throw in another 5d8+10.
Keeping in mind that this is pretty much pure theory crafting unless you roll 3 17+ stats and one more high enough for a decent con. Even then you lose out on Wish etc.
That mostly seems legit to me, assuming you have ridiculous ability scores. The main problem is with unarmed damage. If you are level 14 in wizard then you are most 6 in monk, so unarmed damage would be 1d6. Shadow blade would be a monk weapon.
That pretty much matches. The monk damage die is low at 6th yes, but with Song of Victory , you are adding a +3 or +5 in addition to the Dex damage bonus. I'd rather have 1d6 +10 than 1d10+5.
For this build to be effective, I would reccomend the following:
Pure Wizard/Bladesinger until level 14.
Multi-class into monk for levels 15 - 16.
At level 20 you will be Wizard 18/Monk 2
This won't give you the kensi abilities and extra ki, but the trade off is that you don't loose too much spell progression with the monk dip.
(analysis) You will only have 3 ki, but at 80ish DPR that shouldn't be an issue for you. As a high-level caster this will probably be a tactic that you use for moderate threat encounters so that you can preserve your high-level spell slots. Most of your time should be spent casting spells anyway so I don't imagine you will feel the lack of ki more than the lack of spell progression.
(trade-offs) If you spend 2 levels in monk at this point you will be limited to level 7 spells for a total of 4 levels which in it's self is not so bad. The big loss is that it slows your progression to 9th level spells by 2 levels. There is not a lot that a bladesinger gets from monk at this level except for ki uses and maybe some weapon proficiencies. Not exciting, but Bladesinger does put 3 ki to very good use with Song of Victory.
(wizard play style analysis) By the time that Bladesingers get song of victory their impact in melee can be a reliability if they are concentrating on an important spell. It may be that in most encounters the best options is to avoid melee so that concention checks are avoided as well. But not all combat encounters are equal so this can be effective.
(Big picture analysis) Monk could be taken first, but wisdom and intelligence proficiency are more valuable for wizards than strenght and dexterity. Also Monk could be taken at a lower level but that would slow progression to Song of Victory which is the key componet to this multi-class dip. Ultimately the player gets slightly more by not multi-classing because of how unarmored defense works. But if you do find yourself with a magic item that raises your wisdom score to 19 or 20 at lower levels then unarmored defense combined with bladesong could offer a higher AC than Mage armor (math below).
(math)
Unarmored defense with wisdom of 20 = 15
add dex = 19
add bladesong bonus = 24
Monster attack bonuses at this level tend to be around 11 meaning that they will hit your walking AC on a roll of 13. Since you can cast shield then they will have to roll 18 or higher to hit you. If you use patient defense instead of flury of blows then they will have disadvantage to hit which reduces the chances to hit much lower. And at this point you probably have magical bonuses to AC as well which will stack with unarmored defense.
Sorry if something likelthis is posted elsewhere.
Obviously it is MAD to a high degree requiring maxing Dex, Wis, and Int And still needing decent Con .
The big advantages are:
the Song of victory specifies "Starting at 14th level, you add your Intelligence modifier (minimum of +1) to the damage of your melee weapon attacks while your Bladesong is active."
The sage advice on unarmed strikes is:" The rule on unarmed strikes is an exception: they can be used for melee weapon attacks, despite not being weapons "( https://mobile.twitter.com/JeremyECrawford/status/634388740887085057?ref_src=twsrc^tfw|twcamp^tweetembed&ref_url=https://d-3622668197603214225.ampproject.net/1903141753530/frame.html) per Jeremy Crawford.
That seems pretty clear then that you could use them together. It isn't broke or anything, however it does mean that a monk could be doing 1d8+10 for each of 2 regular attacks and 1d6 +10 for each flurry of blows.average of 56 damage (assuming all hit) with 1 ki point. And that isn't including Haste as an option or a Shadow blade (see below).
The AC potential here is interesting, with the possibility of a 27 while bladesinging and with the +2 Agile Parry bonus. 29 if you have bracers of d. If you wanted to go full on AC crazy you could use all 3 attunement slots for a bracers, a ring of protection, and a cloak of protection and get to 31. If hasted 33.
Shadow blade is an interesting question here: could it be a monk weapon? It seems to fit the requirements. Since you don't get the regular spell progression this spell becomes worth casting at high levels because that is upping the 2 regular attacks to 5d8+10 each, per round you can keep concentration. 10d8+20, +2d6+20 per round as long as slots and concentration and ki hold up. If someone else can haste you, throw in another 5d8+10.
Keeping in mind that this is pretty much pure theory crafting unless you roll 3 17+ stats and one more high enough for a decent con. Even then you lose out on Wish etc.
But how cool would it look!?!
That mostly seems legit to me, assuming you have ridiculous ability scores. The main problem is with unarmed damage. If you are level 14 in wizard then you are most 6 in monk, so unarmed damage would be 1d6. Shadow blade would be a monk weapon.
That pretty much matches. The monk damage die is low at 6th yes, but with Song of Victory , you are adding a +3 or +5 in addition to the Dex damage bonus. I'd rather have 1d6 +10 than 1d10+5.
For this build to be effective, I would reccomend the following:
Pure Wizard/Bladesinger until level 14.
Multi-class into monk for levels 15 - 16.
At level 20 you will be Wizard 18/Monk 2
This won't give you the kensi abilities and extra ki, but the trade off is that you don't loose too much spell progression with the monk dip.
(analysis) You will only have 3 ki, but at 80ish DPR that shouldn't be an issue for you. As a high-level caster this will probably be a tactic that you use for moderate threat encounters so that you can preserve your high-level spell slots. Most of your time should be spent casting spells anyway so I don't imagine you will feel the lack of ki more than the lack of spell progression.
(trade-offs) If you spend 2 levels in monk at this point you will be limited to level 7 spells for a total of 4 levels which in it's self is not so bad. The big loss is that it slows your progression to 9th level spells by 2 levels. There is not a lot that a bladesinger gets from monk at this level except for ki uses and maybe some weapon proficiencies. Not exciting, but Bladesinger does put 3 ki to very good use with Song of Victory.
(wizard play style analysis) By the time that Bladesingers get song of victory their impact in melee can be a reliability if they are concentrating on an important spell. It may be that in most encounters the best options is to avoid melee so that concention checks are avoided as well. But not all combat encounters are equal so this can be effective.
(Big picture analysis) Monk could be taken first, but wisdom and intelligence proficiency are more valuable for wizards than strenght and dexterity. Also Monk could be taken at a lower level but that would slow progression to Song of Victory which is the key componet to this multi-class dip. Ultimately the player gets slightly more by not multi-classing because of how unarmored defense works. But if you do find yourself with a magic item that raises your wisdom score to 19 or 20 at lower levels then unarmored defense combined with bladesong could offer a higher AC than Mage armor (math below).
(math)
Unarmored defense with wisdom of 20 = 15
add dex = 19
add bladesong bonus = 24
Monster attack bonuses at this level tend to be around 11 meaning that they will hit your walking AC on a roll of 13. Since you can cast shield then they will have to roll 18 or higher to hit you. If you use patient defense instead of flury of blows then they will have disadvantage to hit which reduces the chances to hit much lower. And at this point you probably have magical bonuses to AC as well which will stack with unarmored defense.