Centralized motion planning algorithms struggle to scale in multi-arm manipulation, where inter-arm coupling and tight workspaces amplify complexity. We introduce MR-STORM, a distributed sampling-based MPC framework that leverages massively parallel GPU sampling for arm control. Our approach integrates inter-arm collision avoidance via plan-sharing and a dynamic priority scheme to maintain task efficiency. We show empirically that MR-STORM outperforms existing baselines in complex simulation environments and that it transfers effectively to physical hardware. Code, demos and data are available at: https://roboworkshop.github.io/multi-robot-mpc/

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