Understanding the physical and interpersonal constraints that afford cooperation during real-world tasks requires consideration of the fit between the environment and task-relevant dimensions of coactors and the coactors’ fit with each other. In the present study, we examined how cooperation can emerge during ongoing interaction using the simple task of two actors’ moving long wooden planks. The system dynamics showed hysteresis: A past-action mode persisted when both solo and joint actions were possible. Moreover, pairs whose arm spans were both short, both long, or mismatched made action-mode transitions at similar points, when scaled by a relational measure. The relational measure of plank length to arm span was dictated by the pair member with the shorter arm span, who, thus, had a greater need to cooperate during the task. The results suggest that understanding affordances for cooperation requires giving more consideration to constraints imposed by the fit between coactors’ action capabilities.