Existing multi-label classification methods have long suffered from label heterogeneity, where learning a label obscures another. By modeling multi-label classification as a multi-task problem, this issue can be regarded as a negative transfer, which indicates challenges to achieve simultaneously satisfied performance across multiple tasks. In this work, we propose the Hybrid Sharing Query (HSQ), a transformer-based model that introduces the mixture-of-experts architecture to image multi-label classification. HSQ is designed to leverage label correlations while mitigating heterogeneity effectively. To this end, HSQ is incorporated with a fusion expert framework that enables it to optimally combine the strengths of task-specialized experts with shared experts, ultimately enhancing multi-label classification performance across most labels. Extensive experiments are conducted on two benchmark datasets, with the results demonstrating that the proposed method achieves state-of-the-art performance and yields simultaneous improvements across most labels. The code is available at https://github.com/zihao-yin/HSQ