This paper considers a nonlinear pricing framework with both horizontally and vertically differentiated products. By endogenizing the set of consumers served in the market, we are able to study how increased competition affects nonlinear pricing, in particular the market coverage and quality distortions. We characterize the symmetric equilibrium menu of price-quality offers under different market structures. When the market structure moves from monopoly to duopoly, we show that more types of consumers are served and quality distortions decrease. As the market structure becomes more competitive, the effect of increased competition exhibits some non-monotonic features: when the initial competition is not too weak, a further increase in the number of firms leads to more types of consumers being covered and a reduction in quality distortions; when the initial competition is weak, an increase in the number of firms leads to fewer types of consumers being covered, though the effect on quality distortions is not uniform.