Games need separate platinum trophies for single player and multiplayer.

[Kantor]

No. Platinums do not exist to give you a pretty graphic on your trophycard. Platinums exist to keep you playing for a long time- they give you an incentive to do so.

So there should be one platinum per game. The whole POINT is that it is hard to get. If you don't want to play the game fully to get the pretty graphic, that's your loss.