Incorporeal Individuals?

What would it mean for incorporeal entities to be distinct?

For material entities, I can point to such and such in one place, and to another something in another place. So, they must be somehow distinct, even if we can also point to continuity.

Mathematical objects appear to be the best place to look. We distinguish mathematicals by strict definitions; every single such object has a rigorous logical definition which completely determines it, except for the basic objects and axiomata of a given mathematical system. The non-foundational objects are completely determined by their relations to the foundational objects, however; they are separate in a sense, but each one already contains all of the others as well. As soon as you have 2, you have 3, 4, 5, and so on, and the basic theorems of a system already entail everything we could ever prove from them. And the foundational elements again arise from our practical considerations in the material world.

So, mathematical elements are not terribly individuated; in fact, it seems that the main individuation requires matter, and what is non-material is what lacks proper individuation; 2, 3, and so on, are individuals only insofar as we get the concepts of 1 and addition from experience, but insofar as they are simply logical entities, they are not really distinct (as in, it would be logically impossible to have 2 and not 3; same with any two theorems of any mathematical system).

Next would seem to be philosophical psychology: we experience ourselves as individuals, and for many, as non-reducible to bodies. But would we have this individuation without our specific material circumstances? Do we even form unique individuals insofar as we are incorporeal, or is it precisely insofar as we disconnect ourselves from the material world that we become more similar? Aren't our thoughts, our ideas and ideals, our ways of life, things which unite us with others sharing the same?

Formal distinctions, then; maybe there are simply different kinds of incorporeal entities. But this is an unsatisfying reply; I'm asking for what it would mean for incorporeal entities to be distinct, and I am being told that they simply are. But what does that mean? Again, in all physical circumstances, I can point to different spatio-temporal coordinates. In math, I can point to different definitions. I can't just read off my ideas of individuation from these fields and apply them elsewhere; the individuation in those cases in not something separate from how the individuation occurs. Psychology is a bit fuzzy already, and may not be anything distinct from material conditions, but it may be the only way in which we could understand such entities. But even there, it seems that there is less individuation the farther we go from the material.

So, if there were multiple, purely spiritual entities, would it be possible to consider them as purely separate individuals? And a side question: would the idea of a spiritual entity be anything other than that entity? Consider the Pythagorean Theorem: is the thought of the theorem anything other than the theorem, or the theorem itself? And if the latter, how does this relate to the problem of individuation?