Last I saw something like this was in Batman: the Brave and the Bold, but its common.
Has a Small Multiverse that has each world full of the same dopplegangers, but with each world being either its own genre, or obviously connected.
In BBB, Batman has Prime world (his), and Reverse Superhero World where the Joker is the top good guy, and Zombie World. (I've discussed this episode before, but I think I'm bringing out a new aspect of it. The One also had this to some degree, and MJ may have mentioned that.)
Arguably, my attempts to add on a slew of Mary Pipers beyond Alpha and Beta is this.
It'd be interesting to have some sort of cross-dimensional scavenger hunt vs. Gecko, Ltd. (Generic Evil Corporation, Limited.) and their Hunter Teams to find the McGuffin of Pan-Dimensional Dominance. Such a group of good guys or bad guys could be drawn to the verser because they have devices that track other dimensional objects, and they think he's part of the scavenger hunt.
Another idea is that the Genre Multiverse is in balance, but one weight is enough to throw things off...in other words, the arrival of the verser is enough to doom a dozen universes, unless Something is Done.
Basically, have a Noir, A Boring Suburbia, a Medieval, a Western, and about six more worlds, and create some sort of cross-dimensional adventure. It would probably be a lot easier to use clairvoyance on other worlds in the same genre multiverse (or it could be.)
Anyways...