It's generally accepted that the two-weapon fighting style is considered a subpar option. It's disappointing when going by the numbers, the mechanics (just add a small bonus to your one extra attack), and the flavor (it's boring to imagine).
By far the biggest problem is that it doesn't scale. It's ahead for level 3-4, but once you hit level 5 and get your extra attack with fighter, you quickly start falling behind things like Great Weapon Fighting. Mileage against other fighting styles may vary, and while adding in feats like Dual Wielder can help, those other fighting styles have feats as well that negate any attempt to close the gap. All things considered, the two-weapon fighting style just feels and behaves lackluster, and it's turned many away from using it simply because what little flair it gives is not worth the penalties.
So one solution we've been considering at our table to counter that problem is to change the way the two-weapon fighting style itself works. This effect of this change would only be made in relation to extra attacks, keeping all else the same. The original style is written as such:
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.
Under the revision we're considering, this would instead be written as:
Two-Weapon Fighting (Revised)
When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack. Alternatively if you can make an extra attack, you can instead choose to make a number of offhand attacks up to the number of attacks that you take that turn, but without adding your ability modifier to their damage. Opportunity attacks may also add the damage dice from the offhand weapon to the attack.
All in all as I currently see it, this is finally a TWF I'd enjoy playing, and would consider on par in consideration with GWF or Dueling styles, with character style being the deciding factor instead of raw numbers.
So my question is: is there anything I'm missing here that would make this too overpowered or broken?