The aim of this paper is to elucidate the mereological structure of complex states of affairs without relying on the problematic notion of structural universals. For this task tools from graph theory, lattice theory, and the theory of relational systems are employed. Our starting point is the mereology of similarity structures. Since similarity structures are structured sets, their mereology can be considered as a generalization of the mereology of ordinary sets. In general, the mereological systems arising from similarity structures turn out to be not Boolean but Heyting systems. Employing Armstrong’s notion of thick particulars, similarity structures are shown to capture the mereological structure of complex “chemical states of affairs” such as “being butane” or “being isobutane”; structural universals are not needed.