In this article, we explore the connectedness of Responsible Research and Innovation (RRI) profiles and organizational properties of 188 European higher education institutions (HEIs). Empirically we identify three distinct clusters of HEIs in terms of their RRI profile. One cluster is characterized by low RRI uptake, while the other two employ a range of RRI policies and procedures related to gender equality, ethics and public engagement. We find that the RRI active clusters were organizationally very alike, characterized by a rather high degree of research intensity and impact, multi-disciplinary orientation, active participation in Horizon 2020, and by being larger than the RRI passive cluster. We discuss how insights from established theory about change in organizations can be used to explore these similarities and differences.