Fission is a challenge to any theory of personal identity that purports to preserve a tight relation between identity and our practical concerns. The Psychological Criterion will be a clear casualty, for instance.  As for the Biological Criterion, it seems most plausible, in light of fission, to adopt an extreme version of the IDM stance, maintaining (as does Olson 1997, as noted earlier) that our numerical identity just doesn't ground our practical concerns at all (which are instead a function of a “same person relation” that need not adhere to the demands of a strict numerical identity relation).