Effective Class Incremental Segmentation (CIS) requires simultaneously mitigating catastrophic forgetting and ensuring sufficient plasticity to integrate new classes. The inherent conflict above often leads to a back-and-forth, which turns the objective into finding the balance between the performance of previous (old) and incremental (new) classes.To address this conflict, we introduce a novel approach, Conflict Mitigation via Branched Optimization (CoMBO).Within this approach, we present the Query Conflict Reduction module, designed to explicitly refine queries for new classes through lightweight, class-specific adapters.Moreover, we develop two strategies to further mitigate the conflict following the branched structure, i.e., the Half-Learning Half-Distillation (HDHL) over classification probabilities, and the Importance-Based Knowledge Distillation (IKD) over query features.HDHL selectively engages in learning for classification probabilities of queries that match the ground truth of new classes, while aligning unmatched ones to the corresponding old probabilities, thus ensuring retention of old knowledge while absorbing new classes via learning negative samples .Meanwhile, IKD assesses the importance of queries based on their matching degree to old classes, prioritizing the distillation of important features and allowing less critical features to evolve.Extensive experiments in Class Incremental Panoptic and Semantic Segmentation settings have demonstrated the superior performance of CoMBO. The code is available in the supplementary material.