There was a time when I thought of reincarnation much as the Hindus and Theoosphists do, as a transmigrating entity that evolves through successive life times as part of a single stream or continuum. This explanation no longer males sense to me. Even when considering the diversity of my own past lives (according to imaginative and intuitive feelings), there are so many differences that i cannot imagine a single straight line of evolution. It is clear that we each have many selves and many aspects and personalities to our beuing, many streams of consciousness. Some of these lives and personalities may be more advanced, others more primitive, some saintly, some adverse, some with certain intersts and abilities, others totally different.
Several examples of this can already be found in current literature. There is for example Jane Roberts aspect psychology (see e.g. Adventures in Consciousness: An Introduction to Aspect Psychology), probable selves, etc.
There are The Mother's comments on what she refers to as states of consciousness, which combine in are embodied in and make up the individual personality, as aggregates within that personality, but which are not limited to that personality, but come from other personalities, who no doubt have their own aggregates, and so on a la Fritjof Capra's reinterpretation of Geoffrry Chew's Bootstrap Theory of particle physics as the "Dance of Shiva" in his Tao of Physics.
This is also Gurdjieff's idea of many "I"s, although this pertains only to incarnational psychology, not to multiple lifetimes.