The renewed EU agenda for higher education (European Commission, 2017) has emphasized that higher education institutions are not contributing as much as they should to innovation in their regions and countries. The engagement of universities in S3 has shown to be particularly important in countries and regions with weaker regional innovation systems and sub-critical public institutional capacity. The ability of universities to bring together education, research and innovation, places them as particularly important stakeholders to contribute to the research and innovation system. Nevertheless, becoming more engaged in regional innovation policies and S3 requires an important strategic vision and institutional change by HEIs to be able to engage in co-creation dynamics with quadruple helix actors. Moreover, the ability of universities to adjust their working agenda could require some change in their common practices. How they can manage this, mandates a governance framework which can allow for agility from institutes steeped in tradition. The issue of governance is complex, multi-dimensional, and often involves changes in policy, behaviour and outreach for a successful implementation of set objectives. Institutional governance in general and for universities in particular, implies setting in motion or overseeing various institutional processes and regulatory provisions to allow for the planned targets and outcomes to be achieved. The current report proposes an analytical framework for university governance allowing the comparison and benchmarking of governance systems across EU member states, which could serve as guidance for university managers and policy makers to design the institutional incentives and funding programmes for increased engagement in S3. This analytical framework is experimented through a survey involving 74 European universities, the analysis of country annual reports of the Research and innovation observatory (RIO) and the knowledge generated in S2E project covering particularly EU13 countries and the higher education for Smart specialisation initiative (HESS). The main results and limits are commented and discussed with some recommendations.