There are many expectations on Higher Education Institutions (HEI:s) from a range of other actors and organizations to involve and engage in systematic regional innovation and development. Likewise, attempts to achieve such involvement and engagement are many, but success is varied. This paper analyzes the consequences of multifaceted expectations on HEI:s from regional actors, for the involvement and engagement of academics in systematic innovation. Issues of conflict are discovered that constitute obstacles for collaboration. The aim of this study is to highlight disagreements regarding the university’s role in (regional) innovation systems in order to help solve such issues. Theoretically, we approach innovation systems as social systems, and consider systems as subjects of design. Empirically, we have collected policy documents (including figures), interviews, and workshop discussions between representatives for local and regional public administration, intermediary organizations, the university, as well as others, from four Swedish regions. We conclude by providing a set of considerations possible for use when designing the role of the university in an innovation system, thus facilitating a broader and deeper involvement and engagement of academics in innovation processes, or the support of such processes.