Virtual Reality (VR) co-manipulation enables multiple users to collaboratively interact with shared virtual objects. However, existing research treats objects as monolithic entities, overlooking scenarios where users need to manipulate different sub-components simultaneously. This work addresses conflict resolution when users select overlapping vertices (non-disjoint sets) during co-manipulation. We present a comprehensive framework comprising preventive strategies (Object-level and Action-level Restrictions) and reactive strategies (computational conflict resolution). Through two user studies with 76 participants (38 pairs), we evaluated these approaches in collaborative wireframe editing tasks. Study 1 identified Averaging as the optimal computational method, balancing task efficiency with user experience. Study 2 highlighted that Action-level Restriction, which permits overlapping selections but restricts concurrent identical operations, achieved better performance compared to exclusive object locking. Reactive strategies using averaging provided smooth collaboration for experienced users, while second-user priority enabled quick corrections. Our findings indicate that optimal strategy selection depends on task requirements, user expertise, and collaboration patterns. Based on the findings, we provide design implications for developing VR collaboration systems that support flexible sub-components manipulation while maintaining collaborative awareness and minimizing conflicts.

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