Objection 1. It would seem that a notional act can be directed to several Persons, so that there may be several Persons begotten or spirated in God. For whoever has the power of begetting can beget. But the Son has the power of begetting. Therefore He can beget. But He cannot beget Himself: therefore He can beget another son. Therefore there can be several Sons in God.
Objection 2. Further, Augustine says (Contra Maxim. iii, 12): "The Son did not beget a Creator: not that He could not, but that it behoved Him not."
Objection 3. Further, God the Father has greater power to beget than has a created father. But a man can beget several sons. Therefore God can also: the more so that the power of the Father is not diminished after begetting the Son.
On the contrary, In God "that which is possible," and "that which is" do not differ. If, therefore, in God it were possible for there to be several Sons, there would be several Sons. And thus there would be more than three Persons in God; which is heretical.
I answer that, As Athanasius says, in God there is only "one Father, one Son, one Holy Ghost." For this four reasons may be given.
The first reason is in regard to the relations by which alone are the Persons distinct. For since the divine Persons are the relations themselves as subsistent, there would not be several Fathers, or several Sons in God, unless there were more than one paternity, or more than one filiation. And this, indeed, would not be possible except owing to a material distinction: since forms of one species are not multiplied except in respect of matter, which is not in God. Wherefore there can be but one subsistent filiation in God: just as there could be but one subsistent whiteness.
The second reason is taken from the manner of the processions. For God understands and wills all things by one simple act. Wherefore there can be but one person proceeding after the manner of word, which person is the Son; and but one person proceeding after the manner of love, which person is the Holy Ghost.
The third reason is taken from the manner in which the persons proceed. For the persons proceed naturally, as we have said (2), and nature is determined to one.
The fourth reason is taken from the perfection of the divine persons. For this reason is the Son perfect, that the entire divine filiation is contained in Him, and that there is but one Son. The argument is similar in regard to the other persons.
Reply to Objection 1. We can grant, without distinction, that the Son has the same power as the Father; but we cannot grant that the Son has the power "generandi" [of begetting] thus taking "generandi" as the gerund of the active verb, so that the sense would be that the Son has the "power to beget." Just as, although Father and Son have the same being, it does not follow that the Son is the Father, by reason of the notional term added. But if the word "generandi" [of being begotten] is taken as the gerundive of the passive verb, the power "generandi" is in the Son--that is, the power of being begotten. The same is to be said if it be taken as the gerundive of an impersonal verb, so that the sense be "the power of generation"--that is, a power by which it is generated by some person.
Reply to Objection 2. Augustine does not mean to say by those words that the Son could beget a Son: but that if He did not, it was not because He could not, as we shall see later on (42, 6, ad 3).
Reply to Objection 3. Divine perfection and the total absence of matter in God require that there cannot be several Sons in God, as we have explained. Wherefore that there are not several Sons is not due to any lack of begetting power in the Father.
Source: Summa Theologica (New Advent)