Given the strategic role of design when addressing societal changes and its prominence in the circular economy (CE) discourse and practice during the past decade, a plethora of tools and methods is nowadays available to support organizations in the transition from a linear model of production to a circular one. The need for an intersection of CE, corporate sustainability, strategic design and strong sustainability is gaining momentum. Considering (a) the critical voices pointing out several limitations to the CE concept, (b) the call for linking CE to a strong sustainability paradigm and (c) the implementation mechanisms for an effective contribution to sustainable development, the focus of this research is to address the gap in CE and circular design frameworks due to missing elements therein for its successful implementation, using a Delphi method approach. Our results strongly suggest that the current CE and circular design concepts and practices are insufficient to meet the challenge of addressing strong sustainability, and new models are needed. To conclude, a new definition of design for CE in a strong sustainability paradigm and a first approach to the main elements of the new model assisted by guiding principles are proposed.