In the context of developing a new sociology of morality, the article examines such phenomena as moral agency and moral patiency, understood as an actor’s attributed ability to be seen as a subject or object of morally relevant actions. The authors analyze the concept of the “moral dyad” as the most popular general approach that addresses various aspects of attributing moral agency and patiency through mind ascription. We also examine the four key principles of the moral dyad concept: causing harm as a prerequisite for the moral relevance of the action, the inseparable link between mind ascription and moral agency/patiency, the phenomenon of moral typecasting, and the principle of the moral scheme’s completion being a necessity. Based on the criticisms of these basic principles, we consider the prospects for further research in the field of studying these moral qualities of actors of various types. For this purpose, we identify and discuss three key problems of the concept of the “moral dyad”, which, as we argue, should be addressed from a sociological perspective: explaining the moral status of actors in the case of pro-social actions, as well as the moral status of collective (groups, corporations, states, institutions) and non-human (robots, computer algorithms) actors. In conclusion we suggest that focusing on these problems in the context of actual social interactions can become one of the key research areas within the framework of the new sociology of morality.