The minimalist perceptual crossing paradigm has emphasized the essential role of interpersonal dynamics on social understanding. Within the particular case of minimalist interaction, it has been argued that interpersonal processes can constitute social cognition, at least partially, which calls for a paradigm shift in social cognition studies. In this paper, we review several perceptual crossing experiments and their theoretical implications, and propose an original experiment to go beyond strictly dyadic interactions. Whereas past experiments have used objects as distracters of dyadic interaction, our experiment aims at integrating objects themselves as the goal of interpersonal coordination. We asked 24 subjects to participate in a minimalist perceptual crossing experiment where they had to decide, based on their on-line interaction in a one-dimensional digital space, which of the objects they perceived was also perceptible by their partner. The main results suggest that the mutual awareness of a shared object (SO) arises from the quality of sensorimotor coordination between the partners. Indeed, the presence of a SO acts as a simultaneous affordance that attracts and structures individual perceptive activities, giving both partners the opportunity to co-construct a shared world where their respective actions make sense. We discuss our results by way of an enactive account of social cognition, taking the joint perception of a SO as a first step to account for joint attention.