What would happen if we combined the game memory with the game set? (A set is three cards that in each attribute are either all the same or all different. There are four attributes with three possibilities each. For any two set cards there is one and only one other card that would make a set). You'd turn over all the set cards and each player would take a turn flipping over three trying to get a set. It might be too hard, but it could be simplified by trying first holding some attributes constant, for example by only using solids.

Update 2010-07-01: I convinced some people to try playing this, using just the green cards, and it worked pretty well. The main hard part we figuring out when we were done. At first you find sets pretty well, but then there's a long period where no one finds any sets and you're not sure whether you've got them all. We dealt with this by turning the cards over and playing normal set once everyone agreed to.