Crossover - To hell and back

Doomguy: "Noted. I'll have to thank him later."

That'd be a neat co-op game. Enemies you kill in one game (dimension) get sent to the other person's game where your co-op friend can either kill them there or send them back if they're late game enemies with multiple lives in both worlds. Bosses exist in both games at once (requiring both players to reach the end of the level at the same time, and sometimes appear to attack nothing (the other player), which lets you shoot weak points on their back.