This paper uses a highly disaggregated demand system to estimate the degree of substitutability among monetary assets and to address the issue of optimal monetary aggregation in the United States. We address the problems of dimensionality and nonlinearity, estimating a very detailed monetary asset demand system encompassing the full range of assets based on the locally flexible normalized quadratic expenditure function. We treat the concavity property as a maintained hypothesis and provide evidence consistent with neoclassical microeconomic theory. Statistical tests reject the appropriateness of the aggregation assumptions for all the money measures published by the Federal Reserve as well as for a large number of groupings suggested by earlier studies. This supports and reinforces Barnett's (2016) assertion that we should employ the broadest M4 monetary aggregate published by the Center for Financial Stability.JEL codes: C3, C13, C51