Specific emitter identification (SEI) distinguishes emitters by utilizing hardware-induced signal imperfections. However, conventional SEI techniques are primarily designed for single-emitter scenarios. This poses a fundamental limitation in distributed wireless networks, where simultaneous transmissions from multiple emitters result in overlapping signals that conventional single-emitter identification methods cannot effectively handle. To overcome this limitation, we present a specific multi-emitter identification (SMEI) framework via multi-label learning, treating identification as a problem of directly decoding emitter states from overlapping signals. Theoretically, we establish performance bounds using Fano's inequality. Methodologically, the multi-label formulation reduces output dimensionality from exponential to linear scale, thereby substantially decreasing computational complexity. Additionally, we propose an improved SMEI (I-SMEI), which incorporates multi-head attention to effectively capture features in correlated signal combinations. Experimental results demonstrate that SMEI achieves high identification accuracy with a linear computational complexity. Furthermore, the proposed I-SMEI scheme significantly improves identification accuracy across various overlapping scenarios compared to the proposed SMEI and other advanced methods.