Analysis of variance (ANOVA)-type methods are the default tool for the analysis of data with multiple covariates. These tools have been generalized to the multivariate analysis of high-throughput biological datasets, where the main challenge is the problem of small sample size and high dimensionality. However, the existing multi-way analysis methods are not designed for the currently increasingly important experiments where data is obtained from multiple sources. Common examples of such settings include integrated analysis of metabolic and gene expression profiles, or metabolic profiles from several tissues in our case, in a controlled multi-way experimental setup where disease status, medical treatment, gender and time-series are usual covariates.