If we grant that there is one consciousness per nervous system (or maybe 2 if we consider hemispheres) then it seems plausible to me that the nervous system (or brain or body) must be unified in some way.
I want to distinguish "natural" unity vs "observer relative" unity (if there's already terminology for this distinction in philosophy, please post). For example there's a natural unity of my field of experience... many different things appear together... I have no choice over this. Distinguish this from the unity of an "organism". We as human beings decide to categorize matter in certain ways say "inanimate" vs "animate"... but we perform this categorization for convenience. Ultimately, all we have is matter and energy. An organism, or a computer all composed of matter/energy... Why do we take them to be two "unified" things instead of millions of little bits? It's primarily because of "our" interests and it helps us organize. It is conceivable some other type of beings don't perform this categorization and see the world as points/particles of mass/energy.
This distinction is analogous to the one Searle makes between "intrinsic" intentionality and "as-if" intentionality.
So my guess is that if "consciousness" is naturally unified, then the corresponding "matter" involved might be naturally unified also. As far as I know, nobody has identified this unification. There's a "trivial" unification... All matter/energy in the universe interacts by the laws of physics. But if consciousness is unified into separate discrete bins... then my guess is that there's a type of natural unification of matter that also separates into discrete bins. If these bins correspond to brains, then my guess is there's some "natural" unity to brains.
Has any philosopher attacked this issue of finding natural unities in matter? The only thing I can find that could conceivably cause this "natural" unity of the brain is quantum entanglement.