I see the suggestions with additional bullet types.I think it can work, but you can only "bring with you" 4 bullet types to battle, but you have plenty more to choose from in the "load-out area", or something like that.
The "annoying" part is to program the results of all the possible combinations , the amount of combinations increase exponentially.
I LOVE this idea. Many rouguelikes have multiple characters with unique traits so this could be an interesting and unique way to do that.