Objection 1. It would seem that one Divine Person cannot assume two human natures. For the nature assumed in the mystery of Incarnation has no other suppositum than the suppositum of the Divine Person, as is plain from what has been stated above (2, 3,6). Therefore, if we suppose one Person to assume two human natures, there would be one suppositum of two natures of the same species; which would seem to imply a contradiction, for the nature of one species is only multiplied by distinct supposita.
Objection 2. Further, in this hypothesis it could not be said that the Divine Person incarnate was one man, seeing that He would not have one human nature; neither could it be said that there were several, for several men have distinct supposita, whereas in this case there would be only one suppositum. Therefore the aforesaid hypothesis is impossible.
Objection 3. Further, in the mystery of Incarnation the whole Divine Nature is united to the whole nature assumed, i.e. to every part of it, for Christ is "perfect God and perfect man, complete God and complete man," as Damascene says (De Fide Orth. iii, 7). But two human natures cannot be wholly united together, inasmuch as the soul of one would be united to the body of the other; and, again, two bodies would be together, which would give rise to confusion of natures. Therefore it is not possibly for one Divine Person to assume two human natures.
On the contrary, Whatever the Father can do, that also can the Son do. But after Incarnation the Father can still assume a human nature distinct from that which the Son has assumed; for in nothing is the power of the Father or the Son lessened by Incarnation of the Son. Therefore it seems that after Incarnation the Son can assume another human nature distinct from the one He has assumed.
I answer that, What has power for one thing, and no more, has a power limited to one. Now the power of a Divine Person is infinite, nor can it be limited by any created thing. Hence it may not be said that a Divine Person so assumed one human nature as to be unable to assume another. For it would seem to follow from this that the Personality of the Divine Nature was so comprehended by one human nature as to be unable to assume another to its Personality; and this is impossible, for the Uncreated cannot be comprehended by any creature. Hence it is plain that, whether we consider the Divine Person in regard to His power, which is the principle of the union, or in regard to His Personality, which is the term of the union, it has to be said that the Divine Person, over and beyond the human nature which He has assumed, can assume another distinct human nature.
Reply to Objection 1. A created nature is completed in its essentials by its form, which is multiplied according to the division of matter. And hence, if the composition of matter and form constitutes a new suppositum, the consequence is that the nature is multiplied by the multiplication of supposita. But in the mystery of Incarnation the union of form and matter, i.e. of soul and body, does not constitute a new suppositum, as was said above (Article 6). Hence there can be a numerical multitude on the part of the nature, on account of the division of matter, without distinction of supposita.
Reply to Objection 2. It might seem possible to reply that in such a hypothesis it would follow that there were two men by reason of the two natures, just as, on the contrary, the three Persons would be called one man, on account of the one nature assumed, as was said above (6, ad 1). But this does not seem to be true; because we must use words according to the purpose of their signification, which is in relation to our surroundings. Consequently, in order to judge of a word's signification or co-signification, we must consider the things which are around us, in which a word derived from some form is never used in the plural unless there are several supposita. For a man who has on two garments is not said to be "two persons clothed," but "one clothed with two garments"; and whoever has two qualities is designated in the singular as "such by reason of the two qualities." Now the assumed nature is, as it were, a garment, although this similitude does not fit at all points, as has been said above (2, 6, ad 1). And hence, if the Divine Person were to assume two human natures, He would be called, on account of the unity of suppositum, one man having two human natures. Now many men are said to be one people, inasmuch as they have some one thing in common, and not on account of the unity of suppositum. So likewise, if two Divine Persons were to assume one singular human nature, they would be said to be one man, as stated (6, ad 1), not from the unity of suppositum, but because they have some one thing in common.
Reply to Objection 3. The Divine and human natures do not bear the same relation to the one Divine Person, but the Divine Nature is related first of all thereto, inasmuch as It is one with It from eternity; and afterwards the human nature is related to the Divine Person, inasmuch as it is assumed by the Divine Person in time, not indeed that the nature is the Person, but that the Person of God subsists in human nature. For the Son of God is His Godhead, but is not His manhood. And hence, in order that the human nature may be assumed by the Divine Person, the Divine Nature must be united by a personal union with the whole nature assumed, i.e. in all its parts. Now in the two natures assumed there would be a uniform relation to the Divine Person, nor would one assume the other. Hence it would not be necessary for one of them to be altogether united to the other, i.e. all the parts of one with all the parts of the other.
Source: Summa Theologica (New Advent)