This article deals with nonparametric permutation testing methods for repeated observations with multivariate ordered categorical data. Our specific interest is on testing for stochastic dominance, i.e. for a set of restricted alternatives. Several solutions to the univariate stochastic dominance case based on restricted maximum likelihood ratio tests hâve been proposed in the literature. These solutions require quite demanding and stringent assumptions and so are generally criticized: their asymptotic null distributions are mixtures of central chi-squared variables with weights depending on the underlying population distribution F and so the related accuracy is at least difficult or even impossible to assess. Further, testing for stochastic dominance in multivariate settings by the likelihood approach is known to be a much more difficult problem. By working within the conditioning on a set of sufhcient statistics under the null hypothesis and the nonparametric combination (NPC) of dépendent permutation tests it is possible to find exact solutions to some of the related problems. Solutions for multivariate two-sample designs guided by a medical application problem are provided.