Why do you want to do unarmed fighting if you aren't a monk? Some reason not to wield two light weapons so that you can use the "Two Weapon Fighting" rule?
The Tavern Brawler feat allows you to grapple as a bonus action after an unarmed attack.
The Fighter gets a fighting style called Unarmed Fighting, which increases your damage with unarmed attacks (but doesn't grant anything to do with a bonus action).
Can I attack with using unarmed strike and also using my bonus action to do use another unarmed strike?
Not using the normal two-weapon rules.
If you are a monk then you can do it using the monk rules for additional attacks.
So if I take the feat 2 weapon fighting I should talk to my dm first about that?
There's no "two weapon fighting" feat in 5E.
Why do you want to do unarmed fighting if you aren't a monk? Some reason not to wield two light weapons so that you can use the "Two Weapon Fighting" rule?
The Tavern Brawler feat allows you to grapple as a bonus action after an unarmed attack.
The Fighter gets a fighting style called Unarmed Fighting, which increases your damage with unarmed attacks (but doesn't grant anything to do with a bonus action).
Bugbear unarmed fighting then going to multi class to monk with astral self. 100 hands of **** slap haha
If you pick up the Monk class, then yes, you can make unarmed strikes as a bonus action.
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