In several industries, competitive and societal factors have highlighted the need for incubating dedicated radical innovation (RI) capabilities. Traditional approaches to RI strategies have often emphasised either organisational or cognitive aspects, but tend to overlook how these dimensions interact within the organisation. This paper tackles the issue of these interplays by investigating the effects of a creativity-based collaborative method, the KCP Workshops, on the RI capability of a firm. We present an in-depth case study of a leading aeronautics firm that adopted the method to face its RI challenges. While being consistent with prior research and underscoring the impact of organisational settings on creative cognitive processes, our analysis empirically demonstrates a triple capability developed through the KCP Workshops: (1) collectively building a conceivable RI strategy, (2) deploying a monitoring process adapted to the exploration of cognitive breakthroughs, (3) collectively building “emerging creative organisations” at the ecosystem level to support the development of RI strategy. Beyond the performance of the RI capability for commercial applications, these findings underline how the collective design of an RI strategy also involves players in the exploration and establishment of organisational innovations.