Compositional model checking approaches attempt to limit state space explosion by iteratively combining the behaviour of the components in a concurrent system and reducing the result modulo an appropriate equivalence relation. In this article, we consider Labelled Transition Systems (LTSs), in which transitions are labelled by actions, to describe component behaviour, and LTS networks to combine the behaviour of all components in a system. For an equivalence relation to be useful for the compositional model checking of LTS networks, it should be a congruence for the parallel composition operator that is used to combine component behaviour. Such an operator may define synchronisations between the actions of component transitions. 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. Fokkink, Van Glabbeek and Luttik recently proposed a congruence format that implies that this is the case. In parallel, we were the first to prove, by means of the Coq proof assistant, that DPBB is a congruence for the parallel composition of two LTS networks with synchronisation on transition labels. In the current article, we also consider an instance of our parallel composition operator that is both associative and commutative, which are two essential properties for the compositional construction of state spaces. Furthermore, 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.