Is there a possibility that you could get more than one first causes with just the Second Way or am I incorrect?

Specifically, Aquinas gives three arguments that there is one God:

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.

This argument is relying on God's simplicity and specifically on the identity of his essence and his existence. In any contingent thing, essence ("that whereby Socrates is a man") and existence ("what makes Socrates this particular man") are distinct. The existence of something can only be the existence of that thing, although many things can, in general, share an essence. But if there is anything whose essence is its existence, then that essence, like its existence, cannot be shared by multiple things. So there is one God.

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.

This argument seems to rely on the identity of indiscernibles: a presupposition of the inference to the italicized statement. The principle has been contested by subsequent philosophers, who think that two entities could be indiscernible but non-identical. Max Black's counterexample to the principle is a universe that consists of just two indiscernible spheres. The force of this purported counterexample has been discussed previously in Feser's combox; one can either deny that it is a coherent counterexample, or that the spheres are relevantly discernible from each other, or else perhaps opt for an alternative restricted principle that just applies to, say, simple or perfect beings. (Scott, following Brand Blanshard, favored the first two of these approaches. Blanshard thinks that if we are identifying two spheres--that is, if we are suggesting that we can count them, we clearly are discerning a difference between them.)

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.

This is the argument that, I suppose, it is least likely to see someone articulate today, but it is an interesting one. Aquinas's conception of "the world" is something like the collection of things that are causally connected or potentially causally connected. This plays a role in his view of the unity of time as well, for time is the measure of change, and he thought that the unity of time in the world would be measured by the fact that changes in the world are caused by one thing, which itself is caused by God. Since we are no longer inclined to think that there is a single heavenly sphere responsible proximately for all of the change in the world, that argument for the unity of time is no longer available.

This third argument is the one that strikes me least likely to be sound.

To use these after the Second Way, one will need to formulate it in some way so that the pure actuality of the First Efficient Cause is evident, as Aquinas does not in Ia, q. 2, a. 3.

Jason wrote:

Efficient cause is that which brings something into existence or changes it in someway. Like the first way the second way is also a cosmological argument. Here St. Thomas Aquinas is talking about the First Cause which is first as in a series of causes. These series of causes do not go back in time but are right here and now. Thinking that St. Thomas is talking about first cause as in first in time is the most common mistake people make in understanding the second way.

[...]

One way to interpret the Second Way is as a version of the existential proof. The gist of it is that if an x's essence and existence are (really) distinct, some further y is required to unify them.* If, however, that further y's essence and existence are also distinct, it needs some further z to unify it, and so on ad infinitum with nothing ever actually getting unified if everything's essence and existence are distinct.

But if nothing ever gets unified, people, dogs, and cabbages don't exist. So something gets unified. So the regress of unifiers bottoms out in some α whose essence and existence aren't (really) distinct. So by the law of the excluded middle, the regress of unifiers bottoms out in some α whose essence and existence are identical.


*We can replace “unify” with something including the word “cause” if you want, but what's relevant is that the essence and existence are being brought and kept together.