A position in the philosophy of mind that is currently under-represented and under-discussed is Thomistic or hylomorphic dualism. Whereas the tendency of the substance dualist is to identify the person with his soul or mind, the hylomorphic approach identifies the person with a soul-body composite in which soul stands to body as form (morphe) stands to matter (hyle). In a slogan: anima forma corporis: the soul is the form of the body. To be a bit more precise, the soul is the substantial form of the body, a form that makes of the matter it informs a human substance.
This is not a version of substance dualism since soul and body on the hylomorphic scheme are not (primary) substances in their own right. We define a (primary) substance as anything logically (as opposed to causally) capable of independent existence. Fido is then a substance but his soul is not inasmuch as his soul cannot exist on its own. And the same goes for Fido's body: it cannot exist on its own. Fido's corpse can exist on its own, but it is not his body. A dead dog is not a dog: 'dead' in 'dead dog' is an alienans adjective. It functions like 'decoy' in 'decoy duck.' Strictly speaking, a body is a body only when animated by a soul, and a soul is a soul only when animating a body. The composite is what lives and dies, death being the separation of soul and body.
So far, so good.
Now comes the tricky part. For Thomas, the soul of a human being — or the intellective part of the soul of a human being — is not merely a substantial form, but also a subsistent form, a form that can exist on its own. This is the element of Platonism that remains in Thomas's Aristotelianism. This subsistent form can survive separation from the body. The theological motivation for this is perhaps clear: there must be something that bridges the temporal gap between death (separation of soul from body) and resurrection of the body and concomitant reunification of body with soul. That which grounds personal identity over the temporal gap is the soul as subsistent substantial form. Whether there is a need for such a ground is a question that cannot be discussed at the moment.
So although Thomist dualism is distinct from Platonic or Cartesian dualism, it is still a rather robust form of dualism, more robust than the dualism of the epiphenomenalist, say. As long as we don't confuse dualism with substance dualism, there is no reason that I can see for not describing Thomas's hylomorphic theory of mind as dualistic.
So much for a brief sketch of the hylomorphic position. I wish I could report that I find it unproblematic. But I don't. I'll mention one problem now, others later.
How can a substantial form exist apart from that of which it is the form? Is it not necessarily tied to that of which it is the form? After all, it is so tied in the case of non-humans like Fido. Fido is a composite the components of which cannot exist on their own. Why should it be any different in the case of the human soul if the human soul is indeed the form of the human body?
The problem here, in short, is that there is a tension between soul as substantial form and soul as substantial subsistent form. Ontologically, one wants to protest, a form is not the sort of entity that could be subsistent. Necessarily, a form is a form of that of which it is the form. But a subsistent form is possibly such as to exist apart from that of which it is the form. These propositions cannot both be true.
I find it hard to resist the suspicion that what Aquinas has done is implanted Christian elements into the foreign soil of Aristotelianism. Christianity requires that the soul be capable of independent existence. But no form, by its very nature as form, is capable of independent existence. Simply to make an exception in the case of the human soul is wholly unmotivated and ad hoc and inconsistent with hylomorphic ontology.
(Further tantalizing wrinkle: Aquinas describes God as forma formarum, form of all forms, but also as ipsum esse subsistens, self-subsistent existence. So God is a self-subsistent form. He is a form that does not inform anything. More grist for the mill.)