Whole-slide images may contain coexisting lesions, yet weak supervision typically provides only the most severe diagnosis. We formulate this setting as dominant-label multiple instance learning, where the observed label is the maximum-severity element of a latent lesion set. Standard multiclass MIL treats it as a complete one-hot description and therefore suppresses lower-severity evidence whenever it co-occurs with a dominant lesion. We propose DomSet-MIL, a label-aware framework that aligns the annotation mechanism across bag and instance levels. Dominant-Label Censored Likelihood models the reported diagnosis without declaring unreported lesions absent. Severity-Ordered Residual Routing assigns patch evidence from high to low severity and preserves residual support for secondary findings, while top-$q$ pooling links local routing scores to bag prediction. Experiments across natural and controlled settings show that DomSet-MIL achieves state-of-the-art performance in dominant-label prediction while more effectively recovering latent coexisting-lesion evidence. These findings demonstrate that modeling the dominant-label mechanism can improve diagnostic prediction without sacrificing clinically meaningful secondary findings.

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