This does not happen. When we come here to the physical, we bring it all. Soul, Mind, Astral, Etheric. Every lifetime we have ever had is part of us. We may not be in touch with all those aspects but they are with us in this incarnation and not split off somewhere sunning themselves in the Caribbean.
Secondly, there is no point to it. What does happen--rarely--is merging with another person through intense love and devotion. The merging is on a subtle level, like the astral. We really are all One, and love is how that happens.