There is a fairly substantial literature on the manner and extent to which universities engage with society. Such engagement takes many forms: service to underprivileged communities, fair access, contributions to arts and culture, interactions with city developments, collaborations with business and industry, and many more. At first, universities characterised such work as ‘outreach’, or even as ‘third strand’ activities, until it was realised that engagement can neither be a one-way stream nor disengaged from research and teaching. For the engagement agenda to succeed, however, as an academic activity enjoying parity of esteem with research and teaching, there is a question that can no longer be avoided. To what extent is the university’s engagement with society conducted on the university’s own terms, and to what extent (if at all) does the university actually respond to societal needs and demands? I first raised this question in my book The Soul of a University: Why Excellence is Not Enough (Bristol University Press, July 2018). The project being proposed here is a first attempt at finding answers.