Ordination methods such as Principal Component Analysis (PCA) and Principal Coordinates Analysis (PCoA) are commonly applied to microbiome data. These methods are useful exploratory data analysis tools for data reduction and visualization. However, standard ordination methods do not account for repeated measures. For cases in which repeated measures are present, these factors are either averaged over or ignored. Ignoring repeated measures can result in missing important between-subject effects. Three Mode PCA is an approach for dealing with repeated measures in the ordination methods framework. In this work, we extend this method to use non-Euclidean distance measures, which would correspond to a Three Mode PCoA. This method is illustrated by the novel application to microbiome data and is compared to approaches where repeated measures are either assumed to be independent or averaged. Furthermore, this extension may make the choice of distance measures less important after optimization by the Alternating Least Squares algorithm. Future work should focus on handling imbalanced data as well as the extension to N dimensions.