It would be some kind of mixed combat game. Gamers would be divided into teams with different classes. For a team to be successful they must have each class represented and represented well. Here is the key: the classes are decided by the console you were playing it on.

Say for example a Star Wars game:

360 / PS3 - FPS
Wii - Swordplay and Jedi powers
DS / PSP - Strategic command of the AI teammates.

Owners of different systems would have to coorperate. Arguing over consoles would come to an end! Peace would reign on the internet! (Okay not really. Wii owners would have to rub it in that they were the Jedi.)

I'm sure there are much better examples than the one I have given. I actually imagine some senario for Wii players similar to a kicker in the NFL. You kind of make fun of him because he is so different from the rest of the team, but if you have a good one, he is priceless. 

Speaking of Star Wars multiplat games, I think that we need Battlefront III. Seriously, that trailer looked so good! Why, Lucas, why?!!?!

I'm pretty sure that a Battlefront III would fit your description fairly well, though I dunno if they all need to be different. It seems rather limiting to have one class per system. What if I want to be a Jedi, but don't have a Wii? And not to destroy your hopes but I doubt we'll be seeing cross-platform online anytime soon (please correct me if I'm wrong; I haven't heard of any games that do this).

Id buy it

I'm sure you are right. But it would still be cool. Someone could make it happen.