 Now, obviously (P.13ξ) does not qualify as a composition principle in the main sense that we have been considering here, i.e., as a principle that yields a whole out of suitably ξ-related parts. Still, in a derivative sense it does. It asserts the existence of a whole composed of parts that are shared by suitably related entities. Be that as it may, it should be noted that such an additional principle is not innocuous unless ‘ξ’ expresses a condition stronger than mere overlap. For instance, we have said that overlap may be a natural option if one is unwilling to countenance arbitrary scattered sums. It would not, however, be enough to avoid embracing scattered products. Think of two C-shaped objects overlapping at both extremities; their sum would be a one-piece O-shaped object, but their product would consist of two disjoint, separate parts (Bostock 1979: 125). Moreover, and independently, if ξ were just overlap, then (P.13ξ) would be unacceptable for anyone unwilling to embrace mereological extensionality. For it turns out that the Strong Supplementation principle (P.5) would then be derivable from the weaker Supplementation principle (P.4) using only the partial ordering axioms for ‘P’ (in fact, using only Reflexivity and Transitivity; see Simons 1987: 30f). In other words, unless ‘ξ’ expresses a condition stronger than overlap, MM cum (P.13ξ) would automatically include EM. This is perhaps even more remarkable, for on first thought the existence of products would seem to have nothing to do with matters of decomposition, let alone a decomposition principle that is committed to extensionality. On second thought, however, mereological extensionality is really a double-barreled thesis: it says that two wholes cannot be decomposed into the same proper parts but also, by the same token, that two wholes cannot be composed out of the same proper parts. So it is not entirely surprising that as long as proper parthood is well behaved, as per (P.4), extensionality might pop up like this in the presence of substantive composition principles. (It is, however, noteworthy that it already pops up as soon as (P.4) is combined with a seemingly innocent thesis such as the existence of products, so the anti-extensionalist should keep that in mind.)