I have asked a similar question on Philosophy.SE.
Reading Arthur W. Pink's pamphlet Regeneration: Or, the New Birth recently, I was surprised to find that he had a tripartite view of man; and even more surprised to see the nuance in the way he related this to the doctrine of regeneration.
He says, "Man was a tri-partite being" before the Fall. But the Fall "does not mean that either his spirit or soul, or any part thereof, ceased to be, for in Scripture 'death' never signifies annihilation, but is a state of separation." (p. 16 in my copy, which is printed by the Bible Truth Depot, Swengel, Pa.)
But he goes on to say (referencing Galatians 5 and similar passages), "The 'flesh' refers to the degenerate state of man's spirit and soul and body, as the 'spirit' refers to the regenerate state of the spirit and soul—the regeneration of the body being yet future." (18, italics original) This would be a tripartite view much more palatable to those who hold to bipartite view. (The tripartite theory I am more familiar with, associated with Pentecostalism, teaches that at regeneration the spirit is regenerated but not the soul.)
In what works does Pink deal with this doctrine further? The only other work I've read by him is The Attributes of God. How does he distinguish between the soul and the spirit, and what functions does he ascribe to each? What other theologians would agree with this brand of tripartite anthropology?