 A common starting point of the theory of intentionality can be rendered as follows: (1) intentionality is taken to be a feature of minds, (2) minds are to be conceived as individual minds (or minds of individuals), and (3) each individual has his or her own mind. We call this third statement, which is most relevant to the topic at hand, the Individual Ownership Thesis. But how can intentional attitudes be shared in more than a merely distributive sense? Or how can what we call the Irreducibility Claim be true? In meeting the challenge of making irreducibility compatible with individual ownership, a lot depends on where exactly the collectivity is placed in the analysis of collective intentionality.