The European research project Res-AGorA aims to develop a governance framework for Responsible Research and Innovation (RRI). This paper presents the analysis behind our approach. While the various existing RRI governance arrangements do call for a comprehensive framework, the heterogeneity of R&I does not allow to impose a one-size fits all approach. Instead, to design a governance framework which can be applied effectively, we propose to actively build on “RRI in the making”. This is a constructive feature of our approach, enabling anticipatory responses in RRI governance. It needs reflection on an overarching level, which is conceptualised as a ‘meta - governance’ approach that guides the governance of RRI.