 Can perdurantists accept that the lump and statue are distinct, coinciding objects? In principle, yes, but this would be strategically unwise: accepting the possibility of complete coincidence without identity leaves perdurantism with no advantage over the standard endurantist account of coincidence. Perdurantists are better advised to claim that the statue and the lump of clay are one and the same object, then come up with some explanation of why they appear to have different properties. We may say that the object in question could, qua statue, have been made out of a different lump of clay, but could not, qua lump, have been made out of a different lump of clay. There are various ways of explaining what the ‘qua’ clauses are doing in this peculiar claim, and perhaps the most popular explanation involves counterpart theory, a controversial theory about our talk of possibilities. Objections here turn either on problems for counterpart theory, or else on whether a satisfactory theory of how we talk about actual things can ever be compatible with this view.