Buddhists not only believe in reincarnation, but that a single soul can split and be reborn in multiple new incarnations- essentially one soul remanifests itself within more than one being. This is basis of what I call Divergent Soul Theory.
The question is, why would a soul break apart if the purpose of reincarnation is to perfect that soul so that it can achieve higher states? I posit three possible causes for this phenomenon:
1. Will of the Soul.
Bodhisattvas are souls that elect to remain in the cycle of birth and death in order to guide all sentient beings to their ultimate purpose. They are both ascended and manifest. They do this by being whatever they need to be to properly guide beings that need help. Therefore, a Bodhisattva can at once be a god-like figure that is venerated, a strange animal that when sighted causes a moment of awakening, or a person you randomly meet that gives you that one thing you needed to survive the ordeals of your life.
Essentially, the Bodhisattva (or some other advanced soul), chooses upon death to return in numerous forms. By placing a part of the soul into these many forms, the soul can be of greater assistance to the world as well as gain further development by experiencing the world through the lives of other beings.
A soul can experience such a blow by life's experiences that it can actually schism. There are some that believe this occurrence is what causes such things as Multiple Personality Disorder, Schizophrenia, and demon possession. It seems more likely, though, that a soul can slowly be torn apart by living two separate lives. If, say, your work life and your home live cause you to behave as two different people, then eventually you will become two different people.
The goal of reincarnation is to allow the soul to develop into its ultimate form and achieve enlightenment. In order to do this, a soul may need to lose something it gained in an incarnation. Like a flower that blooms more beautifully with pruning, a soul may break apart to lose a part that it does not need, but that another might. The parts of one soul manifest itself into different incarnations, allowing each to be reborn as a soul in its own right.
Buddhism holds that the soul is the whole essence of a being, and the body that soul has is simply its container and a tool used to help that soul grow and change and achieve ultimate enlightenment. Anything can have a soul reincarnated into it, therefore all things are sentient. A soul is aware of the interconnectedness of all things, even if the body housing it is not. Our inner buddha nature seeks to become one with all things, and as such goes from life to life to gain greater understanding. And someday, in some life, the soul within us will learn all it can and achieve ultimate enlightenment and reach its ultimate goal.