Abstract We extend BLP's aggregate discrete-choice model of product differentiation to create more flexibility in the price functional form. We apply a Box-Cox specification, which relaxes the typical unit demand assumption and creates flexibility on demand curvature. The model provides a unifying framework for mixed logit and mixed CES models, while remaining computationally tractable. We provide an illustrative application to the ready-to-eat cereals market. This shows that the cross-sectional relation between price elasticities and average prices per product is more in line with descriptive elasticity patterns, and that substitution between product pairs may be affected to some extent.