I don't think that identity theorists have contributed much to the problem. What makes me "me" in a
particular body, is based on conscious feelings in relation to, or determined by, my body, and an
identity theorist who was an eliminative materialist would deny that there is more to being me than my
body: There is supposedly nothing other, nothing irreducible to body. What makes me is my body,
whether I am conscious or not.
An identity theorist who admits that consciousness is determined by physical body would still have to
hold that I am identical with my body since when my body ceases to exist, so does my
consciousness. While it is logically possible to exist without a body it is difficult to think of coming into
existence without one. On the importance of spatial body, see my answer to Jessica.