Focus theory describes how shared social statuses, beliefs, and places (i.e., foci) can facilitate the formation of social ties, while two-mode projections provide a method for transforming two-mode data on individuals' memberships in foci into a one-mode network of their co-memberships. In this paper, I explore the opposite process: how social ties can facilitate the formation of foci, and how two-mode data can be generated from a one-mode network. Drawing on theories of team, social group, and organization recruitment, I propose three models that describe how such foci might form from the relationships in a social network. I show that these models can be used to generate empirically plausible two-mode networks characterized by positively-skewed degree distributions and an over-representation of four-and six-cycles. I conclude by discussing these models' limitations, and highlighting how they might be used to study twomode networks representing social foci, and to investigate two-mode projection methods.