I’m pretty sure MPD is just two (or more) egos. I don’t see any theoretical problem with having two egos - ego is not real, it’s a fantasy, so it seems perfectly possible to create more than one imaginary persona. Actors can play and switch between multiple personalities. Ego phenomena is roughly the same - the only distinction between ego and acting is that ego is believed to be real, while actors are always aware they’re pretending. So since both personas are believed to be real at the time of experience, one might not have any memory of the other either.

Superego, or, as it is sometimes called “collective unconscious” is also not real, and it’s a little hard to say whether people with MPD share the superego or have a split one as well. I just don’t know much about people with MPD to tell. The defining difference would be whether multiple personalities perceive other people differently or the same. Not treat differently, that’s a given, but perceive differently, on a deep level. For example, if one personality thinks of a person as a kind, empathetic one and another sees the same person as cruel, I would conclude that both ego and superego are split.

I would probably bet that superego is split as well, because superego and ego are reflections of each other - that is, how you perceive other people mainly depends on how you perceive yourself and vice versa.

It could also be somewhat messier or some combination of the two.

Ultimate both ego and superego aren’t real. Only id (the sense of self) is real. Id cannot be split. When you’re hungry, you’re hungry no matter who you think you are right now.