>>This reminds me of that old OLD fanfic, Sleeping With the Girls, where
>>the protagonist finds himself slipping through dimensions but always
>>wakes up in the bed with a random girl protagonist. Never sexy,
>>obviously. And then he goes on an adventure in their world.
>
>i remember that one.... ed baccerra, wasn't it?
>

No, definitely not Ed, although definitely influenced by him.
As I recall the worlds included Tenchi Muyo, Ranma 1/2, Ah! Megami-Sama!, and Sailor Moon... and I'm almost certainly missing a couple.