Not an entire game design, but just an idea:
Remember on Einstein at the Championship when the announcer said the green lights would change between green, blue, and red? How about a game where there are 3 alliances, green, blue, and red. You wouldn't know which alliance you were until right before the match, and over the course of competition you would certainly be each of the alliances at one point. One problem I can think of about three alliances is the set-up for the drive teams. It wouldn't work just to have three drive teams on each end of a rectangular field. Perhaps a triangle-shaped field would work
