The present paper challenges the traditional perspective of the “three-mission university”. We offer an additional perspective based on the idea that university missions are constructs connected by complex relationships. Our empirical study of Spanish public universities corroborates that research (2nd mission) and interaction with the socio-economic environment (3rd mission) mutually benefit each other, however both have a negative effect on teaching (1st mission). In so doing the paper calls for a critical reflection on university engagements with their missions, and on what is to be expected from them vis-à-vis local socio-economic impact.