The aim of this paper is to overcome the problems caused by insufficient price variation in estimating a large demand system. For that, we propose a new form of Stone-Lewbel (SL) cross section prices developed under latent separability that explore individual specific variation in the composition of the bundles of exclusive goods. The estimation of demand system under latent separability needs the choice of at least one exclusive good per group. We estimate Quadratic Almost Ideal Demand System (QAIDS) under weak and latent separability using traditional aggregate price indices and SL prices. Our empirical analysis is based on fifteen non durable goods of a Tunisian Family Expenditure Survey Data. The results show greater differences among effects price and estimates of price elasticities obtained under weak separability and latent separability using both traditional price indices and SL prices. We obtain higher precision of estimates of own price elasticities using SL prices under latent separability.