Story idea

I've been thinking of having a character of mine do a bunch of crossovers. The crossovers I'm thinking of, happen in other writers stories. It would be best if they were just one shot deals that don't have anything to do with the original story, either theirs or mine. I'll ask permission first so there's no foul play. Let's be honest, while reading or writing a story we all had a fantasy where one or more characters went into someone else's story for either fun or to do what they think is a better job of a situation in that one moment. You see it in the comments all the time. Anyway, food for thought.