To the best of my experience, yes, it is entirely possible for a soul, under the proper circumstances, to fracture and become two or more entities separate from one another.
The unfortunate case I refer to is that of a boy I knew in high school, we'll call him Chris. To make a very long story short, I came to love the very parts of him that he wanted to get rid of. He hated me, and he hated the part of himself that I loved. At the time, I was experimenting with psychic vampirism. What I *didn't* know is that my mind is (or was) a lot stronger than the average practitioner's. So there was a pulling force (me) on part of his soul, and a pushing force (him) on the same part. I don't doubt that he probably sat alone in his room, dissociating that part of his soul from himself.
Finally, in what seemed to me a very planned-out event on his part, he transferred the dissociated fragment into me, and blocked all memory of ever having it from his conscious mind. I didn't figure out what had happened until a year or two later, when I became aware of a personality in me that didn't seem to "fit" with my other personalities. It didn't share memory with me, it didn't identify with any of the "normal" archetypes I have for myself, and it didn't seem to have any awareness of me. Now, it does (to an extent) but I think he is confused...I've talked to the people who used to be involved with this and figured out that there's no chance of him ever rejoining with the rest of himself. So I'm stuck wondering what to do with it.
EDIT: Just as an afterthought...I find it kind of ironic how he used to be obsessed with Soul Reaver. <!-- s

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