Parthood is used widely in ontologies across subject domains, specified in a multitude of mereological theories, and even more when combined with topology. To complicate the landscape, decidable languages put restrictions on the language features, so that only fragments of the mereo(topo)logical theories can be represented, even though those full features may be needed to check correctness during modelling. We address these issues by specifying a structured network of theories formulated in multiple logics that are glued together by the various linking constructs of the Distributed Ontology Language, DOL. For the KGEMT mereotopology and its five sub-theories, together with the DL-based OWL species and first- and second-order logic, this network in DOL orchestrates 28 ontologies.