Just after you finish puberty you go into a lab and the scientists take down every detail about you, from your DNA to a full mapping of your brain development. Then every two years or so you go back to have your brain re-mapped so that when you die the scientists can make a clone of your body just after puberty and implant it with all the memories and learning that your brain had the last time you were mapped. (Puberty sucked for me so I'm happy to ditch it from my next life cycle.) Hey presto you can have as many reincarnations of you as you want.
Kind of a mix of "The Island" and Joss Whedon's "Dollhouse."
