If I understand you right, what you are saying is that the soul splits into pieces.
You misunderstand me, then. Metaphor time.
The soul is now a white slab of marble. I am to be born a mortal. At birth, the slab is painted with runes indicating when I was born, what race I am, what gender, etc and placed in my body. I now exist as a mortal, a temporary union of being, body and soul. My being is what the letters on the slab spell out. My body is the construct through which the soul acts. My soul is the vital spark that allows me life in Mundus. As I live, the slab is painted with more runes and patterns as my individual character and identity is developed. Eventually I die. At this point, the body breaks and the slab falls back into the Dreamsleeve, where the pattern I have painted across it is carefully removed. The slab, the soul, is now pure white again and as whole as ever, but I, the pattern, nonetheless remain intact. External. Singular. The pattern is what I am, and it now exists in the final subgradient, that which exists beyond mortal death. The slab is what allowed me to be, and it is used again.