Distributed Description Logics (DDL) is a KR formalism that enables reasoning with multiple ontologies interconnected by directional semantic mapping. Subsumption propagation in DDL from one ontology to another as a result of mappings has been studied, but only for a simplified case when only two ontologies are involved. In this paper we study subsumption propagation in more complex cases, when two ontologies are only connected indirectly, via several other ontologies. We characterize cases in which such subsumption propagation occurs. However, we also identify more complex situations in which subsumption propagation does not occur even if we would expect it. In addition, we propose an adjusted semantics for DDL. Under this semantics, subsumption propagates to remote ontologies to a far greater extent. Other desired properties that have been postulated for DDL, such as directionality and restrained inconsistency propagation are retained.