Bughouse chess might fit the bill in this case. If you're not familiar, there are two boards with four players, with teammates playing opposite colors on each b

Bughouse chess might fit the bill in this case. If you're not familiar, there are two boards with four players, with teammates playing opposite colors on each board. A captured piece on one board can be held in reserve by the teammate and played on any subsequent turn on any open square on the other board.