Alright, so I found a relevant point in W. Norris Clarke’s book The One and the Many. We may encounter some issues, because this comes at the end of the book, after much discussion already regarding act and potency, substance and accidents, the transcendentals, form and matter, essence and existence, intrinsic and extrinsic causes… And furthermore the entire argument of this subsection of this chapter is arguing from any conditioned being to one infinite source of all being, and I’m starting smack dab in the middle, not the beginning. Anyway, there are two points which must be discussed, the first of which is that any being self-sufficient for its own existence must be infinite in perfection, that is, unlimited in its qualitative fullness of all perfections, and therefore no finite being can be self-sufficient.
Why? Let us suppose it were finite. This means it would be one determinate, limited mode of being (limited in qualitative intensity of perfection) among at least several other modes possible, such that at least one higher mode were possible (i.e., this one does not exhaust all possible fullness of perfection). Otherwise, it would not be finite or limited. Now there must be some sufficient reason why the being in question exists in this limited, determinate mode of being and not in some other possible. Why this being, or this whole finite world-system, in fact, and not some other? A principle of selection is needed to select this mode of being from the wider range of possibility and give actual existence to it according to this limited mode (or “essence,” as the metaphysician would call it). But no finite being can do this election of its own essential mode of being and confer existence on itself in this mode. For then it would have the impossible task of preexisting its own determinate actual existence in this mode, picking out what it wills to be before it actually exists, and then conferring actual existence on itself in this mode. All of this is obviously absurd, unintelligible. It follows that no determinate finite being can be the self-sufficient reason for its actual existence as this particular finite being. Therefore it requires an independent efficient cause or source of being to determine it to exist as this finite mode of being. But since no finite cause can ever be self-sufficient, we must eventually come to some infinite (in terms of being the fullness of being/goodness/knowledge) cause or ultimate source of all these finite beings. Something that is not conditioned or limited in any way and simply is unconditioned being/existence.
The same conclusion can be reached by a slightly different approach. Suppose that a finite being were self-sufficient. This would mean that it would have to be the total ultimate source of all attributes within it, including the central, all-embracing perfection of existence itself. Now it does not make sense that the ultimate source of a perfection should possess this perfection in some limited, imperfect way, less than the full plenitude possible of the perfection in question, when it is the very source of this perfection itself. Nor does it make sense that it should deliberately restrict its own possession of this perfection of which it is the ultimate source to some limited degree when it could enjoy the full plenitude of it. The notions of ultimate, self-sufficient source of a perfection and limited possession of the same clash irreconcilably and cancel each other out. No being self-sufficient for its own existence, therefore can possess existence – or any other perfection – only in some limited, incomplete, imperfect way.
Now, there can only be one such infinite being. For suppose there were two such. Then one could not be the other, must be really distinct from the other. But this is impossible unless at least one of the two lacks something that the other one has. Otherwise, they would coincide into total indistinguishable identity. But if either one lacked some positive perfection, it could not also be absolutely infinite in all perfections. If there were two self-sufficient infinite beings, they could not both know each other. For to know another real being one must either have caused it, or been acted on, caused, by it. But in this case one would have to e dependent in some way on the other, and hence could not be self-sufficient for its own existence and all its perfections. Hence there can be only one infinite self-sufficient being.