["JCMS: Journal of Common Market Studies, EarlyView. ", "\nAbstract\nLiterature on policy debates often analyses cases involving either a single or two policy fields, which typically result in stable equilibria, manifesting either as outright rejection of policy proposals, successful institutional change or the entrenchment of divisions into a deadlock. This paper focuses instead on policy debates involving at least three distinct policy fields. Drawing on discursive institutionalism and complex systems theory, we argue that the dynamic interactions between three policy fields generate an endogenous source of persistent instability in the trajectory of policy debates. We conceptualise this dynamic as ‘frame persistent instability’, which occurs when policy debates display discontinuous change and do not culminate in a new equilibrium. We use the metaphor of the three‐body problem to understand the unstable trajectory of debates involving at least three distinct policy fields. To illustrate our argument, we analyse European debates over trade liberalisation, environmental protection and agricultural support using two different levels of analysis. First, using discourse network analysis, we conduct a longitudinal analysis of the evolution of framing dynamics in European public debates. Second, we reconstruct how these three‐body dynamics played out in the specific case of the European Union–Mercosur negotiations using interviews with negotiators and official documents. We find that the complex interactions between these three policy objectives led to the emergence of new discursive frames and the formation of ad‐hoc coalitions. Whilst promoting two objectives at times seemed feasible, achieving all three appeared to be an impossible trinity."]