St. Thomas believed in the unity of the human soul (Compendium cap. 90 tit.):
That there is one soul in one body
Quod unica est anima in uno corpore
He proves this as follows (cap. 90):
it is evident that a man is said to be living because he bas a vegetative soul, that he is called an animal because he has a sensitive soul, and that he is a man because he has an intellectual soul. Consequently, if there were three souls in man, namely, vegetative, sensitive, and rational, man would be placed in a genus because of one of his souls, and in a species because of another. But this is impossible. For thus genus and specific difference would constitute, not what is simply one, but what is one per accidens, or a sort of conglomeration, such as musical and white; but such is not a being that is simply one. Accordingly a man can have only one soul.
patet quod homo dicitur vivens secundum quod habet animam vegetabilem, animal autem secundum quod habet animam sensitivam, homo autem secundum quod habet animam intellectivam. Si igitur sunt tres animæ in homine, scilicet vegetabilis, sensibilis et rationalis, sequitur quod homo secundum aliam animam ponatur in genere, et secundum aliam speciem sortiatur. Hoc autem est impossibile: sic enim ex genere et differentia non fieret unum simpliciter, sed unum per accidens, vel quasi congregatum, sicut musicum et album, quod non est esse unum simpliciter. Necesse est igitur in homine unam tantum animam esse.
He gives some arguments seeming to prove the multiplicity of souls in man, "quæ videntur probare quod in homine sunt plures animæ", one of which tries to show that there must be separate souls for bodily functions as for intellectual functions (cap. 91):
since the operations of the vegetative and sensitive soul are not exercised apart from the body, their principles cannot be without a body. On the other hand, the operation of the intellectual soul is exercised without a body; and so, apparently, no bodily energy can be its cause. Therefore the same soul cannot be vegetative, sensitive, and rational.
cum operationes animæ vegetabilis et sensibilis non sint sine corpore, nec earum principia sine corpore possunt esse; operatio autem animæ intellectivæ est sine corpore, et sic impossibile videtur quod aliqua virtus in corpore sit eius causa. Impossibile igitur videtur quod eadem anima sit vegetabilis, sensibilis et rationalis.
Which he refutes as follows (cap. 92):
in the generation of a man the fetus (conceptum) first lives the life of a plant through the vegetative soul; next, when this form is removed by corruption, it acquires, by a sort of new generation, a sensitive soul and lives the life of an animal; finally, when this soul is in turn removed by corruption, the ultimate and complete form is introduced. This is the rational soul, which comprises within itself whatever perfection was found in the previous forms.
in generatione hominis conceptum quidem primo vivit vita plantae per animam vegetabilem; deinde remota hac forma per corruptionem, acquirit quadam alia generatione animam sensibilem, et vivit vita animalis; deinde remota hac anima per corruptionem, introducitur forma ultima et completa, quae est anima rationalis, comprehendens in se quidquid perfectionis in praecedentibus formis erat.
This is probably his clearest statement of mediate animation or delayed hominization, but it's unclear if this is a temporal or metaphysical succession.
{Though he does seem to refer to the Blessed Virgin before the infusion of her rational soul (III q. 27 a. 2 co.): "ante infusionem animæ rationalis beata virgo sanctificata non fuit", "before the infusion of the rational soul, the Blessed Virgin was not sanctified", because only those possessing a rational soul can be sanctified, but this doesn't prove he thought she could exist without a rational soul; cf. "What is the basis for saying that Aquinas accepted the Immaculate Conception?"}
See Ashley 2006 pp. 344-5 n. 22 for most all the references to St. Thomas regarding human development.
St. Thomas also argues that Christ was animated at conception: Summa Theologica III q. 33.