Could you play a game like Chess, but cooperatively (everyone working together, against the game)?
Everyone has control over 1 or 2 specific piece types, as you play against the board.
(Or, if you have enough players, just a team-based thing.)
Alternatively,
- Everyone may move every pawn.
- HOWEVER, every player has a unique type of “movement” (2 steps straight, diagonal, L-shape, jump over stuff or not, etcetera.)
- Which means you need to coordinate WHO moves WHAT (and when) to reach your goals.