The social dimension of innovation is growing due to unprecedented wicked global challenges we all face, including COVID-19 pandemic. Those challenges in their dynamic complexity require new cross-scale, cross-domain and action-oriented approaches at the universities. I argue that universities need to go beyond their traditional missions and to take an active role in a transformative change by working with their communities and creating real social impact. The fourth mission concept is particularly relevant as it puts emphasis on the universities roles in sustainable development. I propose to reflect on those new roles of universities in the context of quadruple/quintuple helix model that is seen as playing an important role in fostering the shift from technical to social innovations. Social innovation is an element of a regional innovation system, in which the importance of knowledge is not determined exclusively by competitiveness and productivity, but by taking into account the creation of social well-being, the impact on the quality of life and co-creation of knowledge as part of public–private partnerships. By addressing social innovation practices from a perspective of Polish public universities, it fills the gap of relatively few studies on institutional change and incentive structures that influences the ability of universities to engage in social innovation by proposing. I propose to adapt the socially engaged university model that could be a tool for stimulating and strengthening their functions within a modern regional innovation system allowing for an active role of civil society organisations.