The AFR, the Fallacy of Composition, and Underdetermination

A lot of anti-AFR arguments make the charge that it commits the fallacy of composition. My claim is that sometimes the status of the upper-level state follows necessarily from the base-level states, and sometimes it leaves the hopelessly underdetermined. The state of a planet seems to be fully determined by the states of the particles that make up the planet (plus relations to the star it revolves around, etc.) Mental states are, as I see it, hopelessly underdetermined by the physical. The physical states are compatible with numerous mental states, or even a complete lack of mental states entirely.