The information bottleneck principle provides an information-theoretic method for learning a good representation as a trade-off between conciseness and predictive ability, which can reduce information redundancy, eliminate irrelevant and superfluous features, and thus enhance the in-domain generalizability. However, in low-resource or out-of-domain scenarios where the assumption of i.i.d does not necessarily hold true, superfluous (or redundant) relevant features may be supplemental to the mainline features of the model, and be beneficial in making prediction for test dataset with distribution shift. Therefore, instead of squeezing the input information by information bottleneck, we propose to keep as much relevant information as possible in use for making predictions. A three-stage supervised learning framework is designed and implemented to jointly learn the mainline and supplemental features, relieving supplemental features from the suppression of mainline features. Extensive experiments have shown that the learned representations of our method have good in-domain and out-of-domain generalization abilities, especially in low-resource cases.