Social entrepreneurs are said to be intrinsically innovative, but their capabilities to develop social innovations have not be theorized yet. In this paper, we address this “innovation paradox” identified by Peattie and Morley: we explore the role of the purpose as a key factor for social entrepreneurs to design radical innovations. We draw upon a deep longitudinal case study on a firm committed to the fight against malnutrition. Our analysis highlights how this firm has continuously renewed its purpose to open innovative paths and involve new partners. We identify this as the capacity to frame “generative common purposes”, meaning the constant renewal of a conceptual social purpose so that to stimulate collaborative innovation. This opens up new research perspectives on the articulation of innovation processes and social entrepreneurship.