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This work introduces a composite Three-Way application of the High Order Singular Value Decomposition. Two of the three component data matrices are processed by a standard Redundancy Analysis. The remaining “external” data matrix is related to the others in a heterogeneous system of relations, that can be well suited to tensor analysis. The external data are set to be linked with the first matrix, while with the second matrix the relations are explained only through multivariate linear regression. An application introduces the method, based on the official data from the Italian Equitable and Sustainable Well-being indicators.