In this germ of a story idea, the protagonist is capable of asexually reproducing an identical version of itself, which it can then leave in place. the copy will carry on its existence in its own way, beginning as the same individual and then changing due to environment and experience, as all organisms do. Later on the copies meet up with each other.
If a human, imagine yourself on a trip, where you decide to stay, but you also have to return. In this case, you split yourself in two, and then both of the yous carry on with their respective lives from that point forward. Both are exactly you to begin with, but diverge, becoming distinctly different future yous. Would you make the “same” friends? The versions of them that you tend to see everywhere you go? What other parallels can you imagine?
submitted for your consideration
not allowed – neither of these yous are allowed to be “hit men” or otherwise forced to murder each other. also, in a radical divergence from contemporary fiction, rape is not allowed into the plot either.