The 'I' is not the 'soul' but merely the ego (Latin for 'I' btw -- both Freud and Jung were much more relaxed about their terminology than English psychologists and wrote 'Ich' in German. It was English translators who resorted to high-falutin' Latin to make psychology sound 'scientific'....). The sensory consciousness is secondary, a product of the body, not the real being. Even 'scientific' psychology admits that the conscious self is just a stream of impressions and not a real entity. Yet it tries to behave as if it is, and thus all the 'psychological problems' that humans are prone to. So this much is recognize by both modern 'scientific' psychology and traditional religuous/esoteric psychology.
According to Vedic/Buddhist tradition and the Chinese Taoist tradition, even the deeper 'self' ('soul' or whatever you call it) is only an illusion and must ultimately be dissolved. If this 'self' is not a definite thing but a 'phenomenon' like personality does it have to be contained in any one location? Who is to say what forms it may take or how it might relate to the physical world? (Or more appropriately, does it need to relate to the physical world at all? Why does it need to be in a 'location' in extended space-time?)
If there is 'no such thing as time' then how can the same 'soul' have more than one incarnation at all? Aren't ALL incarnations 'simultaneous' in ultimate timeless reality? So the 'soul' already has many different 'streams of consciousness' feeding into it. From a timeless perspective, what difference does it make whether some of those 'streams of consciousness' are closely related in the physical world of space-time? The experience of events in 'time' is a feature of the 'I' not the soul, there is no danger of 'confusion' from too much happening at once. :)
I haven't found anything about this in Buddhist philosophy yet, but both the Cayce material and the Seth material maintain that simultaneous incarnations do occur.