Abstract Epidemiologists sometimes collect multivariate continuous data on a number of subjects and then wish to analyze the relationships and the agreement between these measurements. They may choose to compute the empirical quantiles (e.g., medians or quintiles) of each of these measurements and use these quantities to define the marginal categories of a multidimensional contingency table. Such contingency tables have the empirical multivariate quantile-partitioned (EMQP) distribution, an extension of the bivariate case studied by Borkowf et al. (1997, Biometrics 53, 1054–1069). In this paper, we present the general asymptotic theory for the EMQP distribution and nonparametric large sample procedures to estimate the variances of such tables from observed multivariate data. We define several statistics of interest to epidemiologists that can be calculated from EMQP tables, including the intraclass correlation, and present numerical results for these statistics where the original data come from certain underlying trivariate distributions. We also discuss the relationship of the EMQP distribution to other distributions commonly used in categorical data analysis. In addition, we apply EMQP methods to analyze an example from nutritional epidemiology. Finally, we discuss how EMQP theory and methods can unify the distribution theory and estimation procedures for diverse nonparametric statistics calculated from multivariate ranks or quantile-categories.