Decision making with several choice options is central to cognition. To elucidate the neural mechanisms of such decisions, we investigated a recurrent cortical circuit model in which fluctuating spiking neural dynamics underlie trial-by-trial stochastic decisions. The model encodes a continuous analog stimulus feature and is thus applicable to multiple-choice decisions. Importantly, the continuous network captures similarity between alternatives and possible overlaps in their neural representation. Model simulations accounted for behavioral as well as single-unit neurophysiological data from a recent monkey experiment and revealed testable predictions about the patterns of error rate as a function of the similarity between the correct and actual choices. We also found that the similarity and number of options affect speed and accuracy of responses. A mechanism is proposed for flexible control of speed-accuracy tradeoff, based on a simple top-down signal to the decision circuit that may vary nonmonotonically with the number of choice alternatives.