Rather than just doing the conventional "sidestory" angle, during my playtime with Oblivion I've begun to think it'd be cool to be able to use the PSP while on the commute to work to handle some of the "busy work" in Oblivion - make potions, spells, buy/sell items, enchant items, talk to NPCs and queue up quests, etc. Sort of an abridged Oblivion without the exploration or combat (or maybe just arena combat?) that allows you to strictly fast travel to known, non-dungeon locations. The console game would continue to be everything it is now, but then you could put more emphasis on quests and general exploration during your playtime with the console version.
It wouldn't be much of a game per se, rather a game aid.