A recently developed demand system, nicknamed AIDADS, offers a more general approach to capturing consumption preferences. AIDADS generalizes the LES by assuming marginal budget shares vary indirectly with expenditure. AIDADS is limited by the fact that the subsistence parameters are constant across expenditure. We modify AIDADS by replacing the constant subsistence parameters with a function which varies with utility, and hence expenditure. The modified AIDADS (MAIDADS) allows subsistence levels to vary with expenditure. This model is applied to the 1996 International Consumption Project data. As these data span a wide range of expenditure levels, MAIDADS offers a viable alternative when estimating "global demand systems." Results suggest subsistence values for livestock and other food products vary with expenditure, while those for grain are constant across expenditure.