Co-design projects often include multiple partners from diverse organisations in a Quadruple Helix model for innovation. While literature on co-design and participatory design (PD) projects often focus on how to co-design with end-users or citizens, our paper discusses collaboration issues among citizen, industrial, public and academic partners in a living lab-based co-design project. Through analysis of end-project interviews with these partners, we identify a number of tensions that were negotiated in the course of the project, and identify team management, collaboration and facilitation strategies for putting PD to work among this group of citizen, industrial, public and academic partners. We discuss the conflicting discourses of the Quadruple Helix model and the co-design approach to innovation as a possible reason for such tensions. We understand tensions in PD projects organized in a Quadruple Helix model for innovation as both unavoidable and in some cases even productive in driving forward innovative design.