In this paper, we present a match between two ontologies, DEMO and e3Value, with the aim of bridging the gap between Business Modelling and Enterprise Engineering. The goal is to provide an objective set of concepts for integrating the teleological and ontological perspectives of a system. DEMO contributes to the constructability of a business model, by providing a theory and method for designing and engineering enterprises. E3Value contributes to the justifiability of a given system construction, providing the notion of purpose through value semantics, network context and economic concepts, such as reciprocity. The ontology matching effort was guided to address three essential alignment areas: Value Object, Actor and Transaction. Then, additional elements were added to enrich and further ground the integrated models on theory from both sides. The resulting ontology includes a formal definition of shared core concepts and introduces positive constraints which, we argue, improve system model quality by combining two relevant and complementary approaches.