I don't know why, but these seems to me like an idea that would suit OK Go remarkably well:
Write and record a song, then hand all of the individual instrumental and vocal tracks to 12 different producers. Don't give them any direction beyond "Do what that wilt shall be the whole of the Law." Go ahead and work with them, re-record stuff if needs must, but make sure all the producers are working completely sepearately from each other. Then, voila, a new OK Go album made up of 12 versions of the same song produced by 12 different producers. Is it just me, or does that seem like an OK Go kind of thing?