We introduce within-group external effects in the two-sided singlehoming model of Armstrong (2006). First, we propose a general characterization of the platform access fees at the symmetric equilibrium of the game. Second, we combine this general formulation with a specific modeling of the relationship between buyers and sellers on B2C platforms, so as to analyze how changes in the underlying characteristics of the product market affect the equilibrium of the game. We show that sellers may be better off, and buyers worse off, in markets with more sellers. We also show that sellers and buyers prefer full product differentiation while platforms prefer no differentiation.