Compositional model checking approaches attempt to limit state space explosion by iteratively combining behaviour of some of the components in the system and reducing the result modulo an appropriate equivalence relation. For an equivalence relation to be applicable, it should be a congruence for parallel composition where synchronisations between the components may be introduced. An equivalence relation preserving both safety and liveness properties is divergence-preserving branching bisimilarity (DPBB). It has long been generally assumed that DPBB is a congruence for parallel composition. Recently, a congruence format has been proposed that implies that this is the case [1]. In parallel, we were the first to prove this by means of a proof assistant (Coq) for the parallel composition of Labelled Transition Systems (LTSs) with synchronisation on their common alphabet [2]. In the current article, we remove that restriction. In addition, we show that DPBB is a congruence for LTS networks in which many LTSs are composed in parallel at once with support for multi-party synchronisation. Additionally, we discuss how to safely decompose an existing LTS network into components such that their recomposition is equivalent to the original LTS network. Finally, to demonstrate the effectiveness of compositional model checking with intermediate DPBB reductions, we discuss the results we obtained after having conducted a number of experiments.