Radical non-dispositionalism is the view according to which the actual causal/nomic roles of natural properties are totally irrelevant to their de re modal representation. The major difficulty besetting all forms of radical non-dispositionalism is that the latter allegedly allows the metaphysical possibility of two natural properties swapping their actual causal/nomic roles. The aim of this paper is to provide a plausible solution to that problem. To this end, I describe the necessary steps that a proponent of the view may take to respond to it. I argue that those steps include the rejection of the transworld existence of natural properties and the adoption of a counterpart-theoretic framework for their de re modal representation. I, finally, present two versions of the property-counterpart framework which are consistent with the radical non-dispositionalism.