Objection 1. It would seem that two Divine Persons cannot assume one and the same individual nature. For, this being granted, there would either be several men or one. But not several, for just as one Divine Nature in several Persons does not make several gods, so one human nature in several persons does not make several men. Nor would there be only one man, for one man is "this man," which signifies one person; and hence the distinction of three Divine Persons would be destroyed, which cannot be allowed. Therefore neither two nor three Persons can take one human nature.
Objection 2. Further, the assumption is terminated in the unity of Person, as has been said above (Article 2). But the Father, Son, and Holy Ghost are not one Person. Therefore the three Persons cannot assume one human nature.
Objection 3. Further, Damascene says (De Fide Orth. iii, 3,4), and Augustine (De Trin. i, 11,12,13), that from Incarnation of God the Son it follows that whatever is said of the Son of God is said of the Son of Man, and conversely. Hence, if three Persons were to assume one human nature, it would follow that whatever is said of each of the three Persons would be said of the man; and conversely, what was said of the man could be said of each of the three Persons. Therefore what is proper to the Father, viz. to beget the Son, would be said of the man, and consequently would be said of the Son of God; and this could not be. Therefore it is impossible that the three Persons should assume one human nature.
On the contrary, The Incarnate Person subsists in two natures. But the three Persons can subsist in one Divine Nature. Therefore they can also subsist in one human nature in such a way that the human nature be assumed by the three Persons.
I answer that, As was said above (2, 5, ad 1), by the union of the soul and body in Christ neither a new person is made nor a new hypostasis, but one human nature is assumed to the Divine Person or hypostasis, which, indeed, does not take place by the power of the human nature, but by the power of the Divine Person. Now such is the characteristic of the Divine Persons that one does not exclude another from communicating in the same nature, but only in the same Person. Hence, since in the mystery of Incarnation "the whole reason of the deed is the power of the doer," as Augustine says (Ep. ad Volusianum cxxxvii), we must judge of it in regard to the quality of the Divine Person assuming, and not according to the quality of the human nature assumed. Therefore it is not impossible that two or three Divine Persons should assume one human nature, but it would be impossible for them to assume one human hypostasis or person; thus Anselm says in the book De Concep. Virg. (Cur Deus Homo ii, 9), that "several Persons cannot assume one and the same man to unity of Person."
Reply to Objection 1. In the hypothesis that three Persons assume one human nature, it would be true to say that the three Persons were one man, because of the one human nature. For just as it is now true to say the three Persons are one God on account of the one Divine Nature, so it would be true to say they are one man on account of the one human nature. Nor would "one" imply unity of person, but unity in human nature; for it could not be argued that because the three Persons were one man they were one simply. For nothing hinders our saying that men, who are many simply, are in some respect one, e.g. one people, and as Augustine says (De Trin. vi, 3): "The Spirit of God and the spirit of man are by nature different, but by inherence one spirit results," according to 1 Corinthians 6:17: "He who is joined to the Lord is one spirit."
Reply to Objection 2. In this supposition the human nature would be assumed to the unity, not indeed of one Person, but to the unity of each Person, so that even as the Divine Nature has a natural unity with each Person, so also the human nature would have a unity with each Person by assumption.
Reply to Objection 3. In the mystery of Incarnation, there results a communication of the properties belonging to the nature, because whatever belongs to the nature can be predicated of the Person subsisting in that nature, no matter to which of the natures it may apply. Hence in this hypothesis, of the Person of the Father may be predicated what belongs to the human nature and what belongs to the Divine; and likewise of the Person of the Son and of the Holy Ghost. But what belongs to the Person of the Father by reason of His own Person could not be attributed to the Person of the Son or Holy Ghost on account of the distinction of Persons which would still remain. Therefore it might be said that as the Father was unbegotten, so the man was unbegotten, inasmuch as "man" stood for the Person of the Father. But if one were to go on to say, "The man is unbegotten; the Son is man; therefore the Son is unbegotten," it would be the fallacy of figure of speech or of accident; even as we now say God is unbegotten, because the Father is unbegotten, yet we cannot conclude that the Son is unbegotten, although He is God.
Source: Summa Theologica (New Advent)