Feedbacks within the climate–economy system are complex. The research analyzing the relationship between human activities and the climate is considerable, with particular focus on intra-system feedback effects: environmental tipping points, and climate-triggered social tipping points, like migration, to a lesser extent (Kopp et al., 2016; van Ginkel et al., 2018). Due to their cross-disciplinary nature (Guerrero et al., 2018), two-way interactions between the environment and society, whereby movement in either system can trigger inter-system feedbacks (Lade et al., 2013; Yletyinen et al., 2019) as humans respond to a changing environment thereby further changing the environment, have only recently received attention by a growing inter-disciplinary research community. With the aim of improving climate policy and its tools, such as the social cost of carbon, we describe these social–ecological system (SES) feedbacks and place them in the existing taxonomy for tipping points applied by mainstream climate–economy models. Drawing lessons from SES research and related interdisciplinary literature, we discuss the value of and method by which to modify social-cost integrated assessment models (SC-IAMs), like Nordhaus' Dynamic Integrated Climate Economy. As it is critical that climate policy include these risks to the stability of the climate–economy system, we conclude with a research agenda for the identification, quantification, and integration of climate–society feedbacks into SC-IAMs.