This study presents a novel multi-output classification (MOC) framework designed for domain adaptation in fault diagnosis, addressing challenges posed by partially labeled (PL) target domain dataset and coexisting faults in rotating machinery. Unlike conventional multi-class classification (MCC) approaches, the MOC framework independently classifies the severity of each fault, enhancing diagnostic accuracy. By integrating multi-kernel maximum mean discrepancy loss (MKMMD) and entropy minimization loss (EM), the proposed method improves feature transferability between source and target domains, while frequency layer normalization (FLN) effectively handles stationary vibration signals by leveraging mechanical characteristics. Experimental evaluations across six domain adaptation cases, encompassing partially labeled (PL) scenarios, demonstrate the superior performance of the MOC approach over baseline methods in terms of macro F1 score.