 Does second-order physicalism entail supervenience physicalism? The usual assumption is that it does, but, as Melnyk himself notes at one point (2003, p. 23), there is an issue here having to do with the definition of a second-order property, the property of having some property that has a certain causal or theoretical role. What are the properties involved in spelling out these causal or theoretical roles? If physicalism is true at all, it must be true of these properties as much as any other properties. But then by second-order physicalism, these properties themselves will be either physical or realized by physical properties. If the first option is taken, the second-order physicalist will stand revealed as holding a version of identity physicalism (one level up, as it were), and thus will face the multiple realization objection. If the second option is taken, the second-order physicalist looks committed to an infinite regress, since now we have further properties realized by physical properties and, correlatively, further causal or theoretical roles. To avoid the regress, the second-order physicalist might say that these properties supervene on or are identical to physical properties. But now it hard to see the difference between the realization physicalist and these other doctrines. (For some further discussion of this issue, see Elpidorou 2018a.)