In this article, I examine the argument by which Process Externalism-an interesting empirical theory that echoes 4E's core ideas-undermines Kim's supervenience argument. If mental properties do not depend exclusively on neurological properties but depend on external or extra-cranial properties, mental causation cannot be preempted by or reduced to neurological properties. In this sense, Keijzer and Schouten argue that this theory entails a robust nonreductive materialism (RNM) that vindicates a notion of mental causation. However, I will argue that this maneuver produces different kinds of overdetermination problems that compromise the metaphysical austerity of a materialist theory of cognition and, for this reason, Process Externalism might not be conceived as entailing an RNM. Finally, I will suggest that the theory could be rendered as a moderate reductive account of the cognitive phenomena that would avoid the overdetermination problems that haunt nonreductive accounts of cognition.