I don't think any theory that attempts to divide the world into fundamentally different realms is viable. Such realms can not be isolated, they must be able to interact in some way or otherwise one could never know about their existence. And once one concedes that they must be able to interact, the distinction between the realms becomes essentially not much more than a classification, just as we divide life into animals and plants and particles into bosons and fermions.

And it really does not matter about what kind of realm one thinks - souls, ghosts, gods, mathematical objects. If those objects can not influence our physical world directly or indirectly, then you can not know about their existence in any meaningful way. And the interaction must usually also go both ways to get a sensible thing, for example your soul must be able to affect your body but also what your body experiences must affect your soul.