We analyze the existence of pure strategy symmetric price equilibria in a generalized version of Salop (1979)'s circular model of competition between differentiated products - namely, we allow consumers to purchase more than one brand. When consumers purchase all varieties from which they derive non-negative net utility, there is no competition, so that each firm behaves like an unconstrained monopolist. When each consumers is interested in purchasing an exogenously given number (n) of varieties, we show that there is no pure strategy symmetric price equilibrium in general (for n > 2 with linear transportation costs). In turn, if the limitation on the number of varieties consumers purchase comes from a budget constraint then we obtain a multiplicity of symmetric price equilibria, which can be indexed by the number of varieties consumers purchase in equilibrium.