Given Quine's views on philosophical methodology, he should not have taken the axioms of classical mereology to be "self-evident", or "analytic"; but rather, he should have set out to justify them by what might be broadly called an "inference to the best explanation". He does very little to this end. In particular, he does little to examine alternative theories, to see if there might be anything they could explain better than classical mereology can. I argue that there is something important that needs to be explained, namely, the way that properties "travel around in clusters" (eg. we often know that "when and where there is something with such-and-such property, there is also something with so-and-so other property", and so on). I argue that these clusterings of properties can be given various subtle (broadly "commonsense") explanations using a version of mereology that denies the classical axiom of "extensionality" (that is, denying that two distinct things must have distinct parts). I offer a challenge to the Quinean metaphysics: to show that these "non-extensional" explanations can be replaced by better explanations that use only classical, extensional mereology and set theory.