Respondeo. St. Thomas, in ST I.11.3, gives three reasons for the unity of God.
A. First, here are my scholastic "dissections" of his argument, which I admit are rather sloppy and very open to correction (the text is appended below for you to judge).
1) His absolute simplicity (cf. ST Ia, q. 3).
Major: Whatever is absolutely simple admits of no multiplicity in species.
Minor: God is absolutely simple.
Conclusion: God admits of no multiplicity in species--which means that nothing shares the same species as God.
2) His absolute perfection (Ia, qq. 4-6).
P1: If there were many gods, then there would be differences among them.
P2: If there were differences among the gods, then at least all but one of them are not perfect.
P3: If all but one of them are not perfect, then they are not gods.
P4: But the idea that they are not gods contradicts the first antecedent.
C: There are not many gods.
Defense of P1: This is per se evident. Individuals within a species are distinguished accidentally.
Defense of P2: If there were differences among the gods, then one has a given perfection that the others lack.
Defense of P3: Those that lack such a perfection cannot be called God, because God is absolutely perfect.
Defense of P4: Those entities that we initially posited as being many gods now turn out not to be gods.
3) The unity of the world.
Major: If the world exhibits intrinsic order and unity, then it was ordered and unified by a single mind.
Minor: The world exhibits intrinsic order and unity.
Conclusion: Therefore, the world was ordered and unified by a single mind.
B. Comments. I personally think that the first two are excellent arguments, although I have trouble with the third (at most I can see how it is a probable argument).
To these three, I can add my own, probable argument, based on the principle of parsimony (or what has been called "Ockham's Razor"). Both Aristotle and Aquinas use this principle elsewhere--although never in Ockham's radical form--so I feel free to use it here as well and dare to call it "Thomistic," or at least compatible with Thomism:
Major: If a cause or principle is sufficient for explaining a phenomenon, it is not necessary to posit two or more causes or principles.
Minor: A single first cause or principle (let's call it "God") is sufficient for explaining the phenomenon of the existence and order of the universe.
Conclusion: Therefore, it is not necessary to posit two or more first causes.
As I mentioned, this argument yields probability only, not necessity: it argues that, while there may be many gods, we have no reason to think there are many. The burden of proof is put on those who would want to claim that there are many. In any case, I prefer Aquinas' first two arguments to my own--those two (at least) do conclude that there can only be one God, and this is necessarily the case. Below is Aquinas' text from ST I.11.3c, for reference.
"I answer that, It can be shown from these three sources that God is one.
First from His simplicity. For it is manifest that the reason why any singular thing is "this particular thing" is because it cannot be communicated to many: since that whereby Socrates is a man, can be communicated to many; whereas, what makes him this particular man, is only communicable to one. Therefore, if Socrates were a man by what makes him to be this particular man, as there cannot be many Socrates, so there could not in that way be many men. Now this belongs to God alone; for God Himself is His own nature, as was shown above (Question 3, Article 3). Therefore, in the very same way God is God, and He is this God. Impossible is it therefore that many Gods should exist.
Secondly, this is proved from the infinity of His perfection. For it was shown above (Question 4, Article 2) that God comprehends in Himself the whole perfection of being. If then many gods existed, they would necessarily differ from each other. Something therefore would belong to one which did not belong to another. And if this were a privation, one of them would not be absolutely perfect; but if a perfection, one of them would be without it. So it is impossible for many gods to exist. Hence also the ancient philosophers, constrained as it were by truth, when they asserted an infinite principle, asserted likewise that there was only one such principle.
Thirdly, this is shown from the unity of the world. For all things that exist are seen to be ordered to each other since some serve others. But things that are diverse do not harmonize in the same order, unless they are ordered thereto by one. For many are reduced into one order by one better than by many: because one is the per se cause of one, and many are only the accidental cause of one, inasmuch as they are in some way one. Since therefore what is first is most perfect, and is so per se and not accidentally, it must be that the first which reduces all into one order should be only one. And this one is God."