Although to turn my earlier response on its head, if the number of parallel universes is uncountable infinity, then you get into a strange phenomenon: Most if not all superheroes would exist, not because they are "superheroes", but because the chance is just in their favor in that precise universe. Superman isn't super-strong, but it just happens that every steel-bar he needs to bend was pre-weakened by random rust, he can't fly but a freak tornado throws him where he needs to be without injuring anyone in such a way it looks like he's flying. Of course, several theories reject the infinite universes hypothesis; there's just many, but not infinite.
https://phys.org/news/2009-10-physicists-parallel-universes.html
"By analyzing the mechanism (called "slow roll inflation") that initially generated the quantum fluctuations, the scientists could estimate the number of resulting universes at 10^10^10^7 (a number which is dependent on the model they used). However, this number is limited by other factors, specifically by the limits of the human brain. Since the total amount of information that one individual can absorb in a lifetime is about 10^16 bits, which is equivalent to 10^10^16 configurations, this means that a human brain couldn't distinguish more than 10^10^16 universes." (To be fair, that one is seemingly quite weird result. And if the number of universes is larger or equal to the amount of information our brain can process, doesn't that still mean that every *imaginable* universe is out there? Either way, it's pretty theoretical (in the "unproven gibberish" sense), so I guess dream away!;)

All that matters is that in one universe I am Batman.

*cue Doctor Strange theme here*

It gets pretty confusing stuff, but whichever theory you're following, the key phrase is "set of all POSSIBLE universes". Anime, as we understand it, is certainly not possible, and the same could be said about pretty much all superhero universes. On the other hand, universes with different physics are possible, and people in our universe would be considered "superheroes" in ones where, say, gravitation (or just Earth's mass) was double. (Also, superheroes are ultimately superheroes only because we choose to call them that way)

The Flash is real!?! Multiverse I'm coming xD

No wait, let me get my Doctor!!!

If there are other universes that allow supernatural powers, I suppose. But if they have rules and constraints like ours, then no. I do not think other universes will have supernatural forces, I think even those have to be "natural".

I don't think that's the Multiverse theory.
As I understand it, the Multiverse theory suggests that every possible human condition exists in different but paralel realities.
Thus: short; fat; dumpy nice guy Bobble exists as a tall; slim; evil genius in another reality.
See ?

If it is true, I'm glad I live in this universe. I fucking hate anime