Transnational private sustainability governance, such as eco‐certification, does not operate in a regulatory or jurisdictional vacuum. A public authority may intervene in private governance for various reasons, including to improve private governance’s efficient functioning or to assert public regulatory primacy. This article argues that to properly understand the nature of public‐private governance interactions—whether more competitive or complementary—we need to disaggregate a public authority’s intervention. The article distinguishes between four features of private governance in which a public authority can intervene: standard setting, procedural aspects, supply chain signaling, and compliance incentives. Using the cases of the European Union’s policies on organic agriculture and biofuels production, the article shows that public‐private governance interaction dynamics vary across these private governance features as well as over time. Furthermore, the analysis highlights the importance of active lobbying by private governance actors in influencing these dynamics and the resulting policy outputs.