Cross-modality RGB-infrared (RGB-IR) person re-identification (Re-ID) is a challenging research topic due to the heterogeneity of RGB and infrared images. In this paper, we aim to find some auxiliary modalities, which are homologous with the visible or infrared modalities, to help reduce the modality discrepancy caused by heterogeneous images. Accordingly, a new base-derivative framework is proposed, where base refers to the original visible and infrared modalities, and derivative refers to the two auxiliary modalities that are derived from base. In the proposed framework, the double-modality cross-modal learning problem is reformulated as a four-modality one. After that, the images of all the base and derivative modalities are fed into the feature learning network. With the doubled input images, the learned person features become more discriminative. Furthermore, the proposed framework is optimized by the enhanced intra- and cross-modality constraints with the assistance of two derivative modalities. Experimental results on two publicly available datasets SYSU-MM01 and RegDB show that the proposed method outperforms the other state-of-the-art methods. For instance, we achieve a gain of over 13\% in terms of both Rank-1 and mAP on RegDB dataset.