This paper targets the constitutive basis of social cognition. It begins by describing the traditional and still dominant cognitivist view. Cognitivism assumes internalism about the realisers of social cognition; thus, the embodied and embedded elements of intersubjective engagement are ruled out from playing anything but a basic causal role in an account of social cognition. It then goes on to advance and clarify an alternative to the cognitivist view; namely, an enactive account of social cognition. It does so first by articulating a diachronic constitutive account for how embodied engagement can play a constitutive role in social cognition. It then proceeds to consider an objection; the causal-constitutive fallacy (Adams & Aizawa, 2001, 2008; Block, 2005) against enactive social cognition. The paper proceeds to deflate this objection by establishing that the distinction between constitution and causation is not co-extensive with the distinction between internal constitutive elements and external causal elements. It is then shown that there is a different reason for thinking that an enactive account of social cognition is problematic. We call this objection the 'poverty of the interactional stimulus argument'. This objection turns on the role and characteristics of anticipation in enactive social cognition. It argues that anticipatory processes are mediated by an internally realised model or tacit theory (Carruthers, 2015; Seth, 2015). The final part of this paper dissolves this objection by arguing that it is possible to cast anticipatory processes as orchestrated as well as maintained by sensorimotor couplings between individuals in face-to-face interaction.