This essay presents a puzzle concerning the interaction of epistemic modals, singular terms, and quantifiers. The puzzle poses a number of problems for both static and dynamic theories of epistemic modals. The trouble arises because neither approach takes into account the fact that being possibly thus-and-so (in the epistemic sense of ‘possibly’) is not a trait that an object has in and of itself, but one that an object possesses only relative to a way of thinking of the domain of quantification. I consider two theories that implement this insight: a static version of counterpart theory and a dynamic system of contingent identity. I then consider a variant on the initial puzzle that helps us to choose between the two theories. The variant also sheds light on how the phenomenon discussed in this essay relates to Frege's Puzzle about attitude ascriptions.