Text-to-image person re-identification (TIReID) retrieves pedestrian images of the same identity based on a query text. However, existing methods for TIReID typically treat it as a one-to-one image-text matching problem, only focusing on the relationship between image-text pairs within a view. The many-to-many matching between image-text pairs across views under the same identity is not taken into account, which is one of the main reasons for the poor performance of existing methods. To this end, we propose a simple yet effective framework, called LCR$^2$S, for modeling many-to-many correspondences of the same identity by learning comprehensive representations for both modalities from a novel perspective. We construct a support set for each image (text) by using other images (texts) under the same identity and design a multi-head attentional fusion module to fuse the image (text) and its support set. The resulting enriched image and text features fuse information from multiple views, which are aligned to train a "richer" TIReID model with many-to-many correspondences. Since the support set is unavailable during inference, we propose to distill the knowledge learned by the "richer" model into a lightweight model for inference with a single image/text as input. The lightweight model focuses on semantic association and reasoning of multi-view information, which can generate a comprehensive representation containing multi-view information with only a single-view input to perform accurate text-to-image retrieval during inference. In particular, we use the intra-modal features and inter-modal semantic relations of the "richer" model to supervise the lightweight model to inherit its powerful capability. Extensive experiments demonstrate the effectiveness of LCR$^2$S, and it also achieves new state-of-the-art performance on three popular TIReID datasets.