One theory about what happens in cases of personal fission is this. If a person is split, then there were two colocated people there all along. This fits best with four-dimensionalism. There are, in cases of fission, two people who overlap for a part of their four-dimensional career.
Here is a curious consequence. Suppose that Jim has led a very happy life. Then if I were to split him, I would bring it about that there have always been two happy colocated people there. But increasing the number of happy people makes the world a happier place. So, were I to split Jim, I would make the world have been a happier place. Surely, though, we don't have the power to make the world have been a happier place. So we should reject this four-dimensionalist solution to the problem of fission.