From climate change to disruptive technologies, policymakers constantly face new problems calling for unprecedented institutional solutions. Yet, we still poorly understand the inventive process leading to the emergence of new institutional forms. Existing theories argue that exogenous changes provide incentives and opportunities for institutional invention. However, they fail to explain how the inventive process endogenously structures their emergence. Drawing from complexity theory and Brian Arthur's work on technological inventions, we develop a structural theory recasting the process of inventing new institutions as the combination of pre-existing institutions. Building on three assumptions related to this combinatorial process, we argue that the distance between institutions shapes the emergence of new institutional forms and their regime's trajectory. Following the initial take-off in the number of institutional inventions at the creation of a regime, we expect the rate of institutional inventions over replications will slow down as nearby institutions are combined and accelerate as distant ones are combined. We illustrate these expectations by looking at three regimes: data privacy, climate governance, and investment protection. Together, they showcase how our combinatorial theory can help make sense of the emergence of unprecedented institutions and, more generally, the pace of unfolding complexity in various international regimes.