Gender identity is such a possession. Not to have property in the self is not to be a subject, and so not to have agency. Others writing on the subject, arrive at very similar positions from very different starting points. But we're a little more tightly organized than the multiple personality. We all have things we've forgotten, areas we don't remember.
Different parts do different things.
In different circumstances we're different people. I'm thankful for all my tumbling and athletic and combat training because when I'm in a dangerous physical situation I react so rapidly that only in retrospect can I realize what I've done. A motorcycle accident, for example, I came out of totally uninjured. Just by very fast responses. Multiple personalities develop for protective purposes.