The mission of transforming global food systems into sustainable ones was declared at the 2021 United Nations Food Systems Summit. The rhetoric around this mission pushes a wide range of public, private and civic actors to take significant actions across a range of types of food systems, in order to ensure the achievement of this mission. Specific attention is drawn to the need for these food systems to be inclusive of alternative forms of knowledge, which are often produced outside of the conventional systems of research and innovation. In this article, we explore the challenge of generalising system innovations based on alternative ways of knowing by examining three cases of systems innovation in French food systems. We revisit the recent literature on transformative change, mechanisms of generalisation and intermediation in order to respond to a research gap about the operationalisation of system innovation generalisation. We suggest that four objects of intermediation – knowledge, value(s), infrastructure and rules – work to generalise system innovations. Through a comparative analysis of the intermediated movement of food systems from one situation to the next resulting in turning points along a trajectory, we offer new insights into how transformative change in food systems might occur.