It's fFunny you ask. I don't actually know of any explicitly cooperative pyramid games ... until this morning when I was playing around with some pieces and sort of inadvertently invented a weird game. (Actually my new game may or may not actually be cooperative in nature. It's still really in development. I just made it up this morning, after all. But I think it has interesting prospects as a coop game, anyway.)
Of course, any game that plays 4 players may be played in teams. Martian Coasters, fFor example.
Homeworlds has a semi-cooperative component, in that the good guys are trying to destroy the bad guys. But nobody knows who is on what team, so that gets a bit messy.
In short ... not really, that I know of. Which is really a shame. Great point though!
People!! Where are the coop games!?!?
See http://www.icehousegames.org/wiki/index.php?title=Category:Cooperative for 5 (I haven't played any of them so all I know is that they are in the coop category!)