Research in primate cognition improves our understanding of the evolutionary history of these mental abilities. Large samples from a wide diversity of species are essential to achieve such objectives. However, research on primate cognition usually suffers from very small samples limited to a handful of species, which prevents reliable evolutionary inferences. The ManyPrimates project offers to overcome some of these problems by providing a large-scale collaborative framework for comparative studies on primate cognition. Building on similar initiatives in other areas of psychology, this consortium has already produced a pilot study on short-term memory gathering one of the largest, i.e. 176 individuals, and most diverse, i.e. twelve species from eleven different sites, primate samples to date. Other projects on short-term memory, inhibitory abilities and on inference by exclusion are in progress on large and diverse data sets and represent exciting opportunities to answer still open questions on the origin of the extraordinary cognitive abilities of primates. This paper describes these projects but also the coordination and communication of this collaborative infrastructure and the different ways to contribute to it.