Inspired by the experience of Eastern enlargement, much of the academic debate on EU external relations and the European neighbourhood policy conceives of external influence in terms of the Union’s ability to induce third countries adaptation to predetermined EU norms and regulations. This article introduces a more structural perspective on EU external influence that scrutinizes the institutional extension of sector-specific governance frameworks beyond EU membership. Whereas the traditional notion of influence only focuses on the shift of the EU’s regulatory boundary, extended governance involves also the opening up of organizational structures within the relevant policy field. These new forms of horizontal flexible integration are made possible through the internal flexibilization of the modes of policy-making within the EU, and, in particular, the advent of network governance. Despite its integrative potential, case studies from three policy sectors also document that, under current circumstances, extended network governance is not void of hegemonic traits.