How to take cats together

The aim of this paper is to give mathematical account of an argument of David Lewis in Parts of Classes in defense of universalism in mereology. Specifically we study how to extend models of Core Mereology (following Achille Varzi's terminology) to models in which every collection of parts can be composed into another part. We focus on the two main definitions for mereological compositions and show that any model can be extended to satisfy universalism. We explore which are the "most economical" ways of extending models under various conditions. Remarkably, we show that if the principle of Strong Supplementation is assumed, there is a unique mereological completion, up to isomorphism.