Standard accounts in social ontology and the group cognition debate have typically focused on how collective modes, types, and contents of intentions or representational states must be construed so as to constitute the jointness of the respective agents, cognizers, and their engagements. However, if we take intentions, beliefs, or mental representations all to instantiate some mental properties, then the more basic issue regarding such collective engagements is what it is for groups of individual minds to share a mind. Somewhat surprisingly, this very issue has not received much attention in the respective debates and when it has, typically the outlook has been skeptical or outright negative. In this paper, I argue that it is epistemologically possible for a group of individuals to literally share a single mental unit. In particular, I will put forward and defend what I shall call the zombie conception of group minds.