The success of group foraging in primates is not only determined by ecological and social factors. It is also influenced by cognition. Group foraging success is constrained, for instance, by the challenges of coordination, synchrony and decision-making, and it is enhanced by the ability to share, learn from others and coordinate actions. However, what we currently know about the cognition of individuals in groups comes primarily from experiments on dyads, and what we know of the effect of ecological factors on group dynamics comes from larger wild groups. Our current knowledge of primate group behaviour is thus incomplete. In this review, we identify a gap in our knowledge of primate group dynamics between the dyadic studies on primate cooperation and the large group observational studies of behavioural ecology. We highlight the potential for controlled experimental studies on coordination and cooperation in primate groups. Currently, these exist primarily as studies of dyads, and these do not go far enough in testing limits of group-level behaviours. Controlled studies on primate groups beyond the dyad would be highly informative regarding the bounds of non-human primate collaboration. We look to the literature on how humans behave in groups, specifically from organisational psychology, draw parallels between human and non-human group dynamics and highlight approaches that could be applied across disciplines. Organisational psychology is explicitly concerned with the interactions between individuals in a group and the emergent properties at the group-level of these decisions. We propose that some of the major shortfalls in our understanding of primate social cognition and group dynamics can be filled by using approaches developed by organisational psychologists, particularly regarding the effects of group size and composition on group-level cooperation. To illustrate the potential applications, we provide a list of research questions drawn from organisational psychology that could be applied to non-human primates.