Platform governance scholarship commonly derives the role of the state from its actions as a regulator of platforms: a rule-setter that sets limits and restricts their activities. This article argues that three additional state roles enable and constrain the agency of states to regulate platforms: facilitator, buyer, and producer. Using the EU’s Artificial Intelligence Act as a case study, the article asks: How do different state roles in platform governance shape AI’s regulatory geographies? It answers this research question by outlining two policy dilemmas between those four state roles. First, the EU’s ambition to act as a facilitator of digital markets constrains its scope of interventions as a regulator of platforms. Second, the EU’s deficits in acting as a producer of AI infrastructure exacerbate its dependency as a buyer of Big Tech offerings, especially cloud computing services. The article contends that dilemmas between state roles are not anomalies but defining features of state-platform relations. As generative AI systems gain sophistication, an understanding of how state roles relate to each other helps to navigate their complex governance regimes.