I imagine many who hold to physicalism or materialism do so at least partly out of respect for Occam’s razor: a reluctance to add substantial new metaphysical entities or processes. And indeed, two of my favorite proposals for improving on physicalism posit not only new processes which enable consciousness, causation and the existence of individuals but they also require an additional realm of being beyond our concrete world: a realm of possibility.
In Whitehead’s process theory, each individual (an “actual occasion”) has two poles. It has a physical pole which contains the objective input from antecedent occasions but it also has a mental pole which is able to draw upon a realm of possibility to finalize its becoming. It subsequently becomes part of the objective input for new occasions. The realm of possibility (which Whitehead considered to be God) is the source of true creativity in the system.
In Gregg Rosenberg’s theory, receptive properties unify and connect effective properties (the ones physics explicates are the effective ones) to create real individuals linked in a causal mesh. Receptive properties have an intrinsically experiential aspect which accounts for the origin of consciousness. Rosenberg also says that the fact that effective properties have many potential values implies a metaphysical realm of possibility existing along with the concrete world. The structure of receptive properties in essence chooses among the possibilities.
The existence of a realm of possibility is what makes something like free will possible in these systems, which is another benefit. But the cost is high. In addition to our concrete world, whose individuals require at a minimum a dual-aspect nature to fully explain, we also need in additional world which underlies ours: the realm of the possible.
One thing I always fall back on when I worry that this is too extravagant is the fact that physics itself appears to include a realm of possibility. Today's concrete (classical-looking) state of affairs can be seen as arising from a combination of the concrete past plus "choosing" from the realm of (quantum) possibility.