Discussions of flexibility in organisations generally focus on labour relations, corporate agility, and long-term survival. In much of this writing, flexibility is conceptualised as a feature of organisations and their environments, of organisational strategy and form, and an outcome of characteristics that can be defined and measured. By contrast, we argue that capacities to adapt depend on interpretations of ‘core business’ which is defined by institutional connections established both outside organisations and reproduced within them. This account is informed by social practice theory, the literature on strategy-as-practice, process studies of organisations, and by empirical research conducted in three secondary schools and three hospitals in Northern England. Interviews with thirty-three managers and employees help us to show how the scope for adaptation is constituted and reproduced in the ways that many organisations connect, and in related rhythms and patterns of social life. There are many contexts in which this insight will be important. We focus on the significance of this analysis for the need to modify the timing of energy demand in a lower carbon future. As we show, the relative ability of specific organisations to adapt depends on a broader nexus of interlinking social practices, temporal arrangements, and cross-cutting commitments.