The discussion concerning cooperativity in supported single-atom (SA) catalysis is often limited to the metal-support interaction, which is certainly important, but which is not the only lever for modifying the catalytic performance. Indeed, if the interaction between the SA and the support, which can be seen as a solid ligand presenting its own specificities that fix the first coordination sphere of the metal, plays a central role as in homogeneous catalysis, other factors can strongly contribute to modification of the activity, selectivity and stability of SAs. Therefore, in this mini-review, we briefly summarize the importance of the support (oxide, carbon or a second metal) in SA photo- electro- and thermal-catalysis (support-assisted operation), and concentrate on other types of cooperativities that in some cases enable previously impossible reaction pathways on supported metal SAs. This includes topics that are not specific to SA catalysis, such as metal-ligand or heterobimetallic cooperativity, and cooperativity which is SA-specific such as nanoparticle-SA or mixed-valence SA cooperativity.