Microbiome differential abundance analysis methods for a pair of groups are well established in the literature. However, many microbiome studies involve multiple groups, sometimes even ordered groups, such as stages of a disease, and require different types of comparisons. Standard pairwise comparisons are not only inefficient in terms of power and false discovery rates, but they may not address the scientific question of interest. In this paper, we propose a general framework for performing a wide range of multi-group analyses with covariate adjustments and repeated measures. We demonstrate the effectiveness of our methodology through two real data sets. The first example explores the effects of aridity on the soil microbiome, and the second example investigates the effects of surgical interventions on the microbiome of IBD patients.