The present paper elaborates a critical reflection on the ‘one-size-fits-all’ model which conceptualizesuniversities as centres of excellence in education, research and third mission. It is argued that the short-comings of this perspective are twofold: first, HEIs are treated as homogeneous institutions with equalcapacity to perform and contribute to social engagement; and second, missions are undistinguishablefrom each other. Both features lead to mischaracterizations concerning the role of universities and theircontribution to society. In the view proposed here missions are university strategies linked by complexrelationship of compatibility, and the paper puts in perspective the persisting gap concerning the natureof and the relations across them.