One such writer called it “creating a stem” where the previous time line will continue but a new timeline where the alteration occurred continues from that point. Thus you can travel back to a future that still has you in it but the other time line has another you.
Eventually, he meets more and more of his selves in the same timeline. And as each has a regular lifespan, they are different ages. Some of his selves he gets along with, some not so much. Sometimes he lives with several of his selves.
He even has orgies with his selves, which is really weird. He says it feels good, as he knows how to pleasure himself.
I think the author might have been gay, but perhaps he was signaling that homosexuality is really a form of self-love.