Full Idea
If soul has parts, what holds them together? Not body, because that is united by soul. If a thing unifies the soul, then THAT is the soul (unless it too has parts, which would lead to an infinite regress). Best to say the soul is a unity.
Clarification
'Soul' is the Greek word 'psuché', which covers mind and consciousness and life
Gist of Idea
What unifies the soul would have to be a super-soul, which seems absurd
Source
Aristotle (De Anima [c.329 BCE], 411b10)
Book Reference
Aristotle: 'De Anima (On the Soul)', ed/tr. Lawson-Tancred,H.C. [Penguin 1986], p.153
A Reaction
You don't need a 'thing' to unify something (like a crowd). I say the body holds the soul together, not physically, but because the body's value permeates thought. The body is the focused interest of the soul, like parents kept together by their child.