For a few decades now, firms have had to innovate in cooperation with other organizations. According to the literature on co-innovation, a new form of innovation partnership is now emerging: the exploratory partnership. This type of partnership is the most often established in the early stages of the design process and faces high levels of uncertainty and instability. This paper deals with a strategic design tool, OPERA, based on a recent general design theory named C-K theory. That theory models design reasoning by suggesting a fundamental distinction between concepts (propositions about novel objects) and knowledge (propositions about known objects). According to the theory, the interaction and co-evolution of concepts and knowledge is the main engine through which design progresses. The paper proposes to extend that theory to understand and to act in innovation community context. OPERA enables power holders and design teams to drive innovation projects by providing them with an overview of explored and unexplored concepts and of the activation and production of skills and knowledge. This cartographic system was tested by MINATEC IDEAs Laboratory, a Cross-Industry Exploratory Partnership, over a 15-month period. The innovative platform is composed of partners from different sectors (e.g., energy, technology research center, sports, telecommunications) and aims to build innovative projects and to devise new products and services based on micronanotechnologies. Facing such diversities, actors of MINATEC IDEAs Laboratory used OPERA to see how each project is progressing, the contribution of each project to the global exploration process, and the complementarities between the projects. Such representations enable the committee to identify the main value of a project, any knowledge gaps and the synergies between projects. From a collective point of view, OPERA permits to MINATEC IDEAs Laboratory's members to indicate their favorite concepts and knowledge areas and to estimate converging and diverging interests.