The present paper elaborates a critical reflection on the �one-size-fits-all� model which conceptualizes universities as centres of excellence in education, research and third mission. It is argued that the shortcomings of this perspective are twofold: first, HEIs are treated as homogeneous institutions with equal capacity to perform and contribute to social engagement; and second, missions are undistinguishable from each other. Both features lead to mischaracterizations concerning the role of universities and their contribution to society. In the view proposed here missions are university strategies linked by complex relationship of compatibility, and the paper puts in perspective the persisting gap concerning the nature of and the relations across them.