This note analyses duopoly competition in a two stage (location-price) game, while allowing each firm to establish a couple of outlets. Both the circle and the line model of spatial competition are considered. Our main result is clear-cut: in equilibrium neither firm will take up the opportunity of opening two stores. This is a warning that market segmentation, i.e. competition from multiple outlets, might not be attractive at all, because it entails more intense price competition.