This article introduces a method of multiple hypothesis testing that combines the idea of sequential multiple testing procedures with the structure of resampling methods. The method can be seen as an alternative to the analytic method of Dunnett and Tamhane, which requires a specific distributional form. Resampling incorporates the covariance structure of the data without the need for distributional assumptions. Recent work by Westfall and Young has shown that a step-down resampling method is asymptotically consistent when adjusted p values can be obtained exactly for continuous data. This article shows that in the case of a comparison of two groups on multiple outcomes, those results are generalizable to discrete data where exact adjusted p values are not available. It is shown that the method asymptotically attains the desired level for controlling the experimentwise probability of a type I error.