Stanisław Leśniewski’s mereology was originally conceived as a theory of foundations of mathematics and it is also for this reason that it has philosophical connotations. The ‘philosophical significance’ of mereology was upheld by Bolesław Sobociński who expressed the view in his correspondence with J.M. Bocheński. As he wrote to Bocheński in 1948: “[...] it is interesting that, being such a simple deductive theory, mereology may prove a number of very general theses reminiscent of metaphysical ontology”. The theses which Sobociński had in mind were related to the mereological notion of “the Universe”. Sobociński listed them in the letter adding his philosophical commentary but he did not give proofs for them and did not specify precisely the theory lying behind them. This is what we want to supply in the first part of our paper. We indicate some connections between the notion of the universe and other specific mereological notions. Motivated by Sobociński’s informal suggestions showing his preference for mereology over the axiomatic set theory in application to philosophy we propose to consider Sobociński’s formalism in a new frame which is the ZFM theory—an extension of Zermelo-Fraenkel set theory by mereological axioms, developed by A. Pietruszczak. In this systematic part we investigate reasons of ’philosophical hopes’ mentioned by Sobociński, pinned on the mereological concept of “the Universe”.