Identifying multiple novel classes in an image, known as open-vocabulary multi-label recognition, is a challenging task in computer vision. Recent studies explore the transfer of powerful vision-language models such as CLIP. However, these approaches face two critical challenges: (1) The local semantics of CLIP are disrupted due to its global pre-training objectives, resulting in unreliable regional predictions. (2) The matching property between image regions and candidate labels has been neglected, relying instead on naive feature aggregation such as average pooling, which leads to spurious predictions from irrelevant regions. In this paper, we present RAM (Recover And Match), a novel framework that effectively addresses the above issues. To tackle the first problem, we propose Ladder Local Adapter (LLA) to enforce the model to refocus on its surrounding local regions, recovering local semantics in a memory-friendly way. For the second issue, we propose Knowledge-Constrained Optimal Transport (KCOT) to suppress meaningless matching to non-GT labels by formulating the task as an optimal transport problem. As a result, RAM achieves state-of-the-art performance on NUS-WIDE, MS-COCO, RAPv1, PA100K, MultiScene and MLRSNet datasets from three distinct domains, and shows great potential to boost the existing methods. Code will be made available.