I recall reading a paper that discussed a hypothetical pair black boxes that could violate Bell inequalities better than what's achievable with quantum mechanics.
For example, suppose Alice and Bob are trying to win the (Alice_choice XOR Bob_choice) = (referee_choice_A AND referee_choise_B) game (the CHSH game). Classically the best strategy wins 75% of the time. Quantumly the best strategy wins ~85% of the time. But these hypothetical boxes would win 100% of the time, and the paper talked about what you could do (and not do) with something like that.
I want to reference the paper, but I can't find it!