Currently the limit is 6. That number can be overrun by bonuses (atm, I have 96 laguna burgers and cioppino because of group goals!) but for self-prepping, the ceiling is a mere 6.
I would duel a whole lot more if I could have more of the recipes I most often use ready to go. I'd love for the prep time to be shortened as well (to keep better pace with refill of duel tokens) but having a larger capacity, even just a jump from 6 to 10 on all VIP dishes, would be awesome!