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, the problem can be regarded as a negative transfer that makes it difficult to simultaneously enhance performance across multiple tasks. In this work, we proposed the Hybrid Sharing Query (HSQ), a transformer-based model that introduces the mixture-of-experts architecture to image multi-label classification. Our approach is designed to leverage label correlations while mitigating heterogeneity effectively. To this end, our model is incorporated with a fusion expert framework that enables HSQ to optimally combine the strengths of task-specialized experts with shared experts, ultimately enhancing multi-label classification performance across most labels. We conducted extensive experiments on two benchmark datasets. The results demonstrate that the proposed method achieves state-of-the-art performance and yields simultaneous improvements across most labels. The code will be available upon acceptance.