Okay, so four or more mad scientists, super villains, or D&D bosses design their secret lairs to be full of death traps and weird puzzle shit in order to keep out heroes et al. However, an unfortunate teleportation mishap causes these nefarious individuals to end up in someone else's lair, and they have to find their way out of these unfamiliar death trap-riddled labyrinths.
Mechanics wise, if there are four players, three villains would be trapped in a labyrinth together that would be designed and "run" by the fourth player. They escape when they reach the labyrinth's teleporter (which might be technological or magical, depending on the theme of the labyrinth), after which the players move on to another dungeon/labyrinth/lair. The player who had designed and run the last map is now a villain along with the other characters, trying to escape, and one of the players who had been a villain now runs the labyrinth (and his/her character is no longer with the party for the duration).
So in total, the four players would have to escape from four puzzley mazes, and each player would design and "operate" one of the mazes. The player running the dungeon does the artwork for its duration (I expect the artwork to vary considerably, but as long as the character designs are suitably different, it should be fine). After the final teleporter is reached, all characters return to their home lairs to live happily ever after.
Maybe if a character is killed by a trap or something, they restart at the beginning of that map? Or, to increase comeraderie, the whole party is zapped back to the beginning of the map?
We could also give the villainous characters each a special ability that they could use once per map, like bust down a wall, pick a lock, summon a chicken to hurl into a death trap to see what it does, et cetera. Each special ability would have to be unanimously approved by the other players, of course.
I know it seems like a lot of work, but really each person just designs a single dungeon and some puzzles (or at least some circumventable traps) to keep the characters from reaching the teleporter. For three fourths of the time, each player will be just having fun dungeon crawling.