Homo totus ...

A man, as a rational animal, is a psychosomatic totality. He is not a standalone psuchē. He is not a standalone sōma. Both psuchē  and sōma are abstracted from the ousia that is a man. The danger is (and has ever been) that of concretising the abstractions, resulting in plural ousie rather than a singular ousia. (Cf. the trio of posts on G. Strawson's metaphysics below.) 

Soul-body holism was widespread in pretheoretic ancientry. We find it notably among the ancient Hebrews. The standard Hebrew word for soul in the Old Testament, nephesh, is a word for man altogether. 'The LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life — and man became a living soul [nephesh]' (Genesis 2.7). So a man's soul is his self. (And so it is also in the Koran, the Arabic nafs being cognate with the Hebrew nephesh.) The soul-body Orphism of the (prototheoretic) Greeks is probably the nearest antiquity comes to mind-machine Cartesianism. Aquinas summarises the Orphic-Platonic anthropology as follows: 'Plato claimed that a human being is not a composite of soul and body but that a human being is the soul itself using a body, just as Peter is not a composite of a human being and clothes, but rather a human being using clothes' (Summa contra gentiles, II.57). In this way we are led to a flesh-despising Gnosticism. Take Plato's Cratylus 399d-400c, wherein Socrates is playacting as etymologist (cf. Gorgias 493a, 524b, Phaedo 64a):

SOCRATES: ... Sōma may be variously interpreted, and yet more variously if a little permutation is allowed. For some say that the body is the grave (sema) of the soul which may be thought to be buried in our present life, or again the index of the soul, because the soul gives indications to (semainei) the body. Probably the Orphic poets were the inventors of the name, and they were under the impression that the soul is suffering the punishment of sin, and that the body is an enclosure or prison in which the soul is incarcerated, kept safe (sōma, sozetai), as the name sōma implies, until the penalty is paid.

Neo-Platonic philosophies of man were made normative in the west by Augustine and in the east by Gregory of Nyssa. It was the later rediscovery of Aristotle and of hylemorphism that brought about a shift to an older way of thinking, now systematised. For Aristotle (and thereafter Aquinas et al), the soul cannot be a body—it is in a body. (De anima II.2, 414a.) A man is insouled body, informed matter. And there is much to say for hylemorphism. (It is adductive, not reductive. It explains without explaining away. And so on.) But Aristotelian hylemorphism is also theory-heavy. Nevertheless, it seems the best thing we've got, comparatively.

Lately I've been reading Wolfhart Pannenberg's systematics, and here I've found a reaffirmation of my feelings. He writes: 'Of all the philosophical positions held in antiquity, only the Aristotelian approach could lead to the right conclusion' (II.184). But he goes on thereafter to name his many qualms. R.W. Jenson says much the same thing, that hylemorphism is 'a solution that is [qualifiedly] satisfactory,' but that theology has not generally 'been up to the subtlety' thereof (II.110 of his systematics).

On today's much-trumpeted neuroscientism, we are not insouled bodies (ad modum Aristotle and Aquinas) but inskulled brains. And here, again, are two ousie. It's a brain-body dualism. However, as P.M.S. Hacker notes, brains are organs, not organisms:

'It makes no sense to apply psychological predicates such as "thinks," "remembers," "perceives," "imagines," "wants," "decides," "feels happy," and so forth to the brain. It is a mistake to apply predicates that signify attributes of an animal as a living whole to its parts — a mereological fallacy. Just as it is a mistake to ascribe the property of keeping time to the fusée of an eighteenth-century table clock [...] so too it is a mistake to ascribe to a person's brain the property of thinking that it is raining or of deciding to take an umbrella' (in Human Nature: A Categorical Framework, p. 306).

Just so. And as for Pannenberg:

'Only in the field of intersubjectivity and in consequence of the awareness of the I-relativity of one's own self-consciousness can a distinction between made between body and soul. Over against the soul as the inner world of consciousness stands the body, which, like the things of the world and in distinction from the inner world of my consciousness, is there for others as well as myself. It is tempting to regard the inner world of the consciousness as the true I in distinction from the body. But this is unduly to restrict the concept of the soul as well as that of the ego. In pointing to the speaker, the word "I" always indicates the physical individuality of the speaker. If we are to view the living body as insouled inasmuch as it is living, then the term "soul" must cover more than the inner world of the consciousness. It must also include the unconscious, which is related to one's own corporeality and its history' (II.194).