In recent years, weakly supervised object detection (WSOD) has attracted much attention due to its low labeling cost. The success of recent WSOD models is often ascribed to the two-stage multi-class classification (MCC) task, i.e., multiple instance learning and online classification refinement. Despite achieving non-trivial progresses, these methods overlook potential classification ambiguities between these two MCC tasks and fail to leverage their unique strengths. In this work, we introduce a novel WSOD framework to ameliorate these two issues. For one thing, we propose a self-classification enhancement module that integrates intra-class binary classification (ICBC) to bridge the gap between the two distinct MCC tasks. The ICBC task enhances the network's discrimination between positive and mis-located samples in a class-wise manner and forges a mutually reinforcing relationship with the MCC task. For another, we propose a self-classification correction algorithm during inference, which combines the results of both MCC tasks to effectively reduce the mis-classified predictions. Extensive experiments on the prevalent VOC 2007 & 2012 datasets demonstrate the superior performance of our framework.