Oligopoly models are usually analyzed in the context of two firms anticipating that market outcomes would be qualitatively similar in the case of three or more firms. This is not an exception in the literature on Hotelling's location-then-price competition. In this paper, we show that the main findings in Hotelling's duopoly, brand bunching and the max-min principle of product differentiation no longer hold once three or more firms are allowed to enter the market. That is, oligopolists with three or more firms proliferate brands and neither maximize nor minimize product differentiation.