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 pre-empted 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.