Recent experimental progress is once again producing a huge quantity of data in various areas of biology, in particular on protein interactions. In order to extract meaningful information from this data, researchers typically use a graph representation to which they apply network alignment tools. Because of the combinatorial difficulty of the network alignment problem, most of the algorithms developed so far are heuristics, and the exact ones are of no use in practice on large numbers of networks. In this paper, we propose a unified scheme on the question of network alignment and we present a new algorithm, C3Part-M, based on the work by Boyer et al., that is much more efficient than the original one in the case of multiple networks. We compare it as concerns protein-protein interaction networks to a recently proposed alignment tool, NetworkBLAST-M, and show that we recover similar results, while using a different but exact approach.