While models of sympatric speciation are motivated in part by multi-species adaptive radiations such as the Cameroon crater lake cichlids, existing models have focused on bifurcation into a single pair of daughter species. This paper shows that a familiar model of sympatric speciation, driven by intraspecific competition and assortative mating based on ecological characters values, can yield multiple daughter species if individual niche widths are sufficiently restricted. Surprisingly, the multi-species outcome is not produced by successive bifurcation events, but by simultaneous divergence resulting in a hard polytomy. This result is sensitive to a number of assumptions, whose violation may prevent speciation. In some cases when speciation fails, the population instead ends in a state that closely resembles incipient species pairs, with an ecological polymorphism and partial reproductive isolation. However, this polymorphism is stable and does not lead to complete reproductive isolation, suggesting that empirical cases of incipient species pairs may not always end in speciation.