A generalization of the methods for analyzing bivariate dichotomous data from a stratified two-stage cluster sample (Marques and Koch, 1992) is presented in this paper. This development includes the joint estimation of means for marginal distributions and a set of correlation measures for intra-cluster association for the respective outcomes of each response criterion and for correlation among response criteria for units sharing the same cluster in a multivariate polytomous data setting. The methodology is illustrated with a medical example of clinical effects of topical corticosteroids on healthy skin.2512539