Tl;dr: individual souls are parts of the hypostasis Soul, which as discursive thought hypostasized, is both ontologically prior to, and, as a whole, present in each individual soul.
In chapter 3 of his Plotinus on the Soul, Damian Caluori takes up the second of the two claims made in the opening chapter, namely that the hypostasis Soul is necessary to account for the unity of all souls. He examines the special kind of unity shared by all souls through a careful discussion of the Platonist notion of a one-and-many, and the import of this notion for thinking about the relations of whole to parts, genus to species, and more specifically of Intellect to individual intellects and Soul to souls. Soul, Intellect, and genera all turn out to be wholes of the same kind, namely a one-and-many.
The notion of a one-and-many is, very briefly, the notion of a whole that is, strictly speaking, not identical with the sum of its parts. Plato regards such wholes as the only true wholes in fact, since “part” and “whole” are essentially correlative notions: there can be parts if and only if, there is some one thing, i.e., a whole, of which they are parts. No true whole, in this sense, is “reducible” to its parts. The dominant Platonist view, from the Old Academy onward, regarded genera as wholes of this kind, with subgenera/species as thier parts. The key distinction here being that genera—as Forms—are not only distinct from thier parts, they are, for Platonists, the ontologically prior principles of thier parts (i.e., the subgenrera under them). This notion of a whole that is not only distinct from its parts, but is the ontologically prior principle of its parts, is the necessary background for understanding the relation of individual intellects and souls to thier respective hypostases in Plotinus.
In IV.9.5.15 Plotinus likens the relationship of Intellect and intellects, and Soul and souls, to that of a science and its theorems. He has in mind deductive, axiomatic sciences like geometry, not modern empirical sciences like biology. Six crucial points can be extracted from what he says here about the science-theorem relationship:
(1) a science is a whole in some way consisting of theorems as its parts.
(2) a science is not merely a set of theorems (i.e., it is a “one-and-many”)
(3) a science is prior to, and the principle of, its parts. (Here the science prior to the deduction of its theorems is identical to its fundamental axioms. The fundamental axioms constitute the science as a whole prior to the derivation of any theorems).
(4) the science actually (as opposed to potentially) contains all its parts. (i.e., once derived, the theorems are all within the science as a whole).
(5) the whole science is potentially (as opposed to actually) contained within each theorem. (i.e., Since each theorem has an essential deductive relationship to every other, it is possible in principle to deduce the whole science from each theorem, hence each theorem potentially contains the whole science).
(6) each theorem is individuated (i.e., distinguished from every other) by its particular derivation from the axioms and/or other theorems. It is the specific theorem it is by virtue of its relation to all the others and to the science as a whole.
What each of these six points says about the relationship of theorems to thier science, is true of both the relationship of individual intellects to Intellect and individual souls to Soul. Both Intellect and Soul are wholes in some way consisting of individual intellects and souls as thier parts. Nevertheless, both hypostases are more than—distinct from—from their parts. Indeed, as Intellectual contemplation hypostasized, Intellect is the principle of each individual intellect. Soul, as discursive thinking hypostasized, is similarly the principle of each individual Soul. Both Intellect and Soul contain all individual intellects and souls respectively; and each individual intellect and each individual soul contains the whole of thier respective hypostasis in the following way: Intellect is nothing other than intellectual contemplation itself. As such it is, as a whole, essentially involved in the activity of each individual Intellect. Ditto for Soul, which is identical with discursive thinking itself, and therefore present as a whole in the discursive activity of each individual soul. The key difference here is that Intellect and Soul are actually as opposed to potentially, in each individual intellect/soul, whereas the whole science is only potentially contained in (i.e., deducible from) each theorem. Finally each individual Intellect is distinct from all other individual intellects in virtue of its focusing on a part of the World of Forms (i.e., it contemplates the Form it is identical with). The distinction between Intellect and individual intellects here is that the former neither thinks anything in particular (it thinks reality/being quite generally), and relies on nothing else in it’s essential activity (since it just is intellectual contemplation itself), whereas individual intellects essentially depend on Intellect for thier essential activity.
When Caluori turns to discuss the individuation of souls, he focuses only on the Soul as discursive practical thinking (i.e., as providential care/concern for the sensible world/bodies), omitting discussion of how souls may be individuated at the higher level of discursive theoretical contemplation of the World of Forms. This, to me, seems to leave a gap in the picture, since, as he says himself the Soul as theoretical contemplation is in each individual soul no less than the Soul as discursive practical/providential thinking. Nevertheless, his discussion of how individual souls are individuated by being a particular aspect of Soul’s divine providence is helpful as far as it goes. As Caluori explains, “Each body has a particular role to play in the whole of the providential arrangement of the sensible world. Each soul, in thinking about the role its body has to play, thereby focuses on one particular aspect of the providential arrangement.” (p.88). So just as each individual Intellect is individuated in being that aspect of Intellect focused on the particular aspect of the World of Forms it is identical with, each individual Soul is individuated (at least in terms of it’s demiurgic/providential function) by being the aspect of Soul’s providential thinking particularly focused on the aspect of the sensible world it is concerned with.