Have played a board game called Bunny Kingdoms a few times. I've only ever played it with two players. Would want to play with more to see if it makes the game more fun. I think it is pretty good though.
Played another game, forgot what it was called. Was cooperative, and I played it with 3 players, but you can have as many players as there is abilities in the game, as they are divided among the players. Those abilities are: directional movement (up, down, left, right), climbing escalators, opening new parts of the map, teleporting, etc. You basically got to collect 4 items, and escape a mall, before the time runs out (in the form of an egg timer, which you can flip over a limited amount of times, if you land on the appropriate square). You can't communicate beyond moving a pawn-shaped object to the person who you believe must make an action. Was pretty fun. Games are generally quick. Hardest part is opening up all the map to collect all the items, as that is where most of the potential conflict in people's game plans occurs. The escape part is pretty easy. There are multiple scenarios though, and I only played one scenario, so perhaps there is other ways to play this game that is different to what I described.