I get it now. You're saying that the relativism of how one may define one's personal identity is so great that, in a quantum multiverse, even whether you are splitting into multiple selves or not is a matter of how you define yourself.

Still, that's not the end of it, because then we can ask exactly what parts of the wavefunction are "potential person-parts". I may have some freedom to choose whether a particular object, trait, thought, or state of mind that once existed or that could exist is "part of me", but at some level there has to be an objective correspondence between "person-parts" and "wavefunction-parts".

You may be a self-defining process, but the point of materialism is that this self-defining process is not something separate from the wavefunction which then freely chooses which parts of the wavefunction are going to count as "part of me"; the self-defining process is a part of the wavefunction, and the choosing about what to identify with, is just part of wavefunction dynamics. Eventually you have to ground the whole thing in physics rather than in cognition. Any thoughts on how that works?