Numerous disciplines study the nature of social cognition. Also, in philosophy of mind, there are discourses about socio-cognitive abilities, such as joint action, mindreading, and commitment. However, the so-called standard notions require demanding conditions, which leads to the fact that, for example, abilities of young children and non-human animals cannot be captured by this terminology. By introducing minimal notions, a step has been taken to capture a greater variety of phenomena in the field of social cognition. In this way, current empirical findings can be connected to the theoretical work in philosophy. However, when one characterizes minimal and standard notions by a dichotomous interpretation of a two-system approach, quite a few instances are still falling through the conceptual net. This paper will demonstrate how many instances remain neglected and explore the challenges to develop a disjunctive conceptual schema that can capture the varieties of socio-cognitive abilities.