The notion of indirect separability is exploited to derive a new multistage demand system. The model allows a consistent parameterization of demand relations at various budgeting stages and it fulfills the requirement of flexibility while satisfying separability globally. Two propositions are derived to characterize flexible and separable functional forms, which lead to the specification of a flexible and separable translog (FAST) demand system. The model is particularly attractive for modeling large complete demand systems, and is illustrated with an application to Canadian food demand.