Canonical analysis, a generalization of multiple regression to multiple-response variables, is widely used in ecology. Because these models often involve many parameters (one slope per response per predictor), they pose challenges to model interpretation. Among these challenges, we lack quantitative frameworks for estimating the overall importance of single predictors in multi-response regression models. Here we demonstrate that commonality analysis and hierarchical partitioning, widely used for both estimating predictor importance and improving the interpretation of single-response regression models, are related and complementary frameworks that can be expanded for the analysis of multiple-response models. In this application, we (a) demonstrate the mathematical links between commonality analysis, variation and hierarchical partitioning; (b) generalize these frameworks to allow the analysis of any number of predictor variables or groups of predictor variables as in the case of variation partitioning; and (c) introduce and demonstrate the implementation of these generalized frameworks in the R package rdacca.hp.