Efforts to promote the adoption and scale up of health system innovations must contend with existing institutional context. But there are no commonly used frameworks to ensure that the insights of actors involved in such institutional efforts connect to one another. To test and modify a potential framework – the ‘four-by-four’ framework – we interviewed researcher-entrepreneurs involved in the unfolding story of the cardiovascular Polypill. The framework has four types/level of institution that affect adoption and scale up – 1) informal institutions (L1 – e.g., social norms), 2) formal institutions (L2 – e.g., government policies and regulation), 3) organisational structures (L3 – e.g., organisational boards and mission), and 4) everyday exchange (L4 – e.g., service delivery); vis-à-vis four potential entrepreneurial strategies in response – 1) abide by existing institutions, 2) evade them, 3) alter them, and/or 4) exit entrepreneurial action. Using this framework, we conducted a realist-informed analysis to understand how context (i.e., institutions) and mechanism (i.e., entrepreneurial strategies) influence each other to shape outcomes (i.e., adoption and scale up). We found that researcher-entrepreneurs began with efforts to abide with existing institutions but encountered institutional obstacles at each level. Efforts to abide were followed by seeking to evade and/or alter unfavourable institutions, with greater success evading and/or altering lower (L3 and L4) than upper (L1 and L2) institutions. Exit considerations followed the failure of evade or alter. Shifts between strategies was propelled by learning. The ‘four-by-four’ framework can be used as a scaffold to generate narratives of adoption or scale up efforts, a sensitising tool to prospectively map out contingencies, and a matrix to synthesise narratives and experiences across multiple innovations or settings. Used in these ways, the ‘four-by-four’ framework can help to optimise the transferability and cumulation of insights on how to promote the adoption and scale up of health system innovations.