What I did was add a feature called "off-hand attack". If you take the two-weapon fighting style you can take an extra attack with your second weapon as an off-hand attack and it does not require a bonus action. If you don't have the fighting style it still requires a bonus action. Likewise the extra unarmed strike from the monk's martial arts is also an off-hand attack that does not uses a bonus action. Using Flurry of Blows still requires a bonus action, but it increases from 2 unarmed strikes to 3 unarmed strikes at level 11. Finally, any attack taken as a bonus action counts as an off-hand attack.No, what we need is for the additional attack from TWF to be part of your Action, not a bonus action. It will ruin exactly nothing about the game to do this.
Of course when I made this rule you couldn't just take a feat to get the fighting style, but I'm not sure if I will change it or not. Two-weapon fighting is under-powered. I don't know if this makes it overpowered or not.