Human rights in global value chains have become a key field of study in international law and corporate governance. The analysis often starts with a gap – a ‘governance gap’ in human rights protection. This pragmatic starting point calls for pragmatic solutions: better corporate compliance and more accountability. While this goes a long way in addressing corporate misconduct, the global corporate form, its power and legitimation in transnationally generating and appropriating value tend to become naturalized phenomena. Moreover, the effects of accountability agendas on corporate power and legitimation are hardly considered. Instead, I propose to address the ‘human rights problem’ by understanding the corporation and its networks as consequences of international politics – conceptualized as inter-societal multiplicity. The multiplicity lens offers a possibility to replace the governance gap with a productive conception of inter-societal conditions and can complement the focus on accountability and compliance. I conclude the article by tentatively sketching three important consequences of such a starting point for defining the problem of human rights in global value chains: the international dimensions of the division of labour under competitive conditions, the legitimation of corporate practices and the production of knowledge for their regulation.