I'm 3/4 through Journey of Souls (see previous post) and found some interesting clues about parallel lives, but no huge Earth-shattering new information.
The author of Journey of Souls, Michael Newton, is a hypnotherapist who regressed people back to their life between lives. I finally read the chapter last night about the client who discussed briefly the concept of parallel lives.
This client explained that sometimes a soul will choose to split and live parallel lives, working on similar issues in two different bodies and in two different places, but at overlapping times. I didn't sense from his description, however, that these are Twin Souls as described by Plato, Rumi, or the Huna. He didn't mention a desire to meet his other half, only that working on issues in parallel lives helps to move one faster along the spiritual path.
I'm not finished with the book yet. Perhaps there will be more to learn. I'll keep you posted.