This article generalizes continuum regression (CR) in the hope that regressors “jointly constructed” for several predictands might improve on the separate prediction of individual predictands. The generalization developed is a mixture of principal components regression and de Jong's modification of partial least squares for multiple predictands. The balance of ingredients can be chosen by cross-validation, as can the number of regressors constructed. The new method has been tested on real and simulated data. The indications are that conditions for the superiority of the joint approach may be rare in practice.