Open innovation will have an important role to play in recovering from the aftermath of the coronavirus and it has already made a crucial contribution. The prism of COVID-19 (“COVID” hereafter) has made more vivid both the complexity and unpredictability of managing innovation. This article considers why today’s open, intrinsically unpredictable business environments require updated theories for managing innovation. Concept formation lies at the heart of all social science progress and in this paper, we propose a new concept to accurately reflect the turbulence and complexity of managing open innovation in a post-COVID world. We argue that the innovator’s dilemma—a still influential argument that suggests exploiting current resources necessarily reduces the likelihood of successful exploration for new resources—is an increasingly problematic theoretic anchor. Furthermore, the prescription based on this line of thinking that organizational leaders should foster ambidextrous capabilities is increasingly suspect as leadership is more broadly shared and organizational processes become less easily dichotomized and controllable. We argue that the operating context for organizations is now so complex and ambiguous that it is time to revisit and revise the widely accepted concept of “ambidexterity” and we describe the updated and expanded construct as Multidexterity. “Multidexterity” is the organizational ability to simultaneously carry out multiple search and selection activities based on diverse strategic logics and levels of knowledge to generate a portfolio of innovative outcomes. We describe a number of case studies of extreme and unique collaboration to underpin our revised concept. Our paper reveals the advantages of the updated view, outlining the fresh insights it can generate. We conclude by setting out an agenda for future research and suggesting that joint empirical research by academics and practitioners is needed to further develop this approach to innovation.