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We propose a game-theoretic approach to generalizing the classical Schelling model. At the core of our model are two features that did not receive much attention before. First, we allow multiple individuals to occupy the same location. Second, each individual’s choice of location is influenced by their social network neighbors that also choose the same location. In addition, an individual’s choice is influenced by others in the adjacent locations in a network-structured way, which captures the main spirit of the classical Schelling model and its numerous extensions. Our solution concept is a stable configuration represented as a pure-strategy Nash equilibrium (PSNE). We show that even for various special cases of the problem, computing or counting PSNE is provably hard. We give algorithms for computing PSNE, including efficient algorithms for several special cases. We highlight some of the attractive features of our model, such as predicting very few PSNE, through experiments.