In complex large-scale experiments, in addition to simultaneously considering a large number of features, multiple hypotheses are often being tested for each feature. This leads to a problem of multi-dimensional multiple testing. For example, in gene expression studies over ordered categories (such as time-course or dose-response experiments), interest is often in testing differential expression across several categories for each gene. In this paper, we consider a framework for testing multiple sets of hypothesis, which can be applied to a wide range of problems.