The viewpoint variability across a network of non-overlapping cameras is a challenging problem affecting person re-identification performance. In this paper, we investigate how to mitigate the cross-view ambiguity by learning highly discriminative deep features under the supervision of a novel loss function. The proposed objective is made up of two terms, the steering meta center term and the enhancing centers dispersion term, that steer the training process to mining effective intra-class and inter-class relationships in the feature domain of the identities. The effect of our loss supervision is to generate a more expanded feature space of compact classes where the overall level of the inter-identities' interference is reduced. Compared with the existing metric learning techniques, this approach has the advantage of achieving a better optimization because it jointly learns the embedding and the metric contextually. Our technique, by dismissing side-sources of performance gain, proves to enhance the CNN invariance to viewpoint without incurring increased training complexity (like in Siamese or triplet networks) and outperforms many related state-of-the-art techniques on Market-1501 and CUHK03.