The Gap Problem Addressed Again

Suppose one accepts the existence of a First Cause of some sort. Based on this, in addition to some rather uncontroversial modal axioms, I believe we can justifiably "close the gap," as it were, between First Cause and God. The entire argument - let's call it the Modal Thomistic Cosmological Argument (MTCA) - might be stated as follows:

1. Dependent things exist.
2. Every dependent thing has a cause. (E.g., every dependent thing derives its existence from that in which it is dependent)
3. If there is no First Cause, then nothing will be caused.
4. Therefore, a First Cause exists. (From 1 and 3)
5. Every limited thing has the potential to be caused.
6. A First Cause does not have the potential to be caused. (E.g., It is not possible that a First Cause is caused)
7. Hence, a First Cause must be unlimited. (From 5 and 6 - in other words, a First Cause cannot be limited, since limited things are possibly caused; and if a First Cause were caused, it wouldn't be first, which is a contradiction)
8. Whatever is unlimited is supreme.
9. Therefore, a Supreme Being exists.

I can see no reason to doubt (1)-(7). I've detailed on multiple occasions why I believe a First Cause exists, and (5)-(7), I think, are analytical truths or at least easily inferable from what we know through observation of limited entities. This leaves us with premise (8). "Supremacy" is marked by two features: 1) it must be unlimited; and 2) it must be unique. Part of what we mean by "supremacy" is unlimitedness, so our main focus will be on whether this unlimited First Cause is one or many.

Consider the idea of multiple unlimited entities. If there truly were more than one - let's call two of them X and Y - then in order for X and Y to be distinct, X would have to lack something that Y possesses, or vice-versa. However, a thing can only lack something if it is limited. Therefore, whatever is unlimited is by necessity unique. This, of course, matches our definition of a "Supreme Being," which is what we mean by "God."