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Zero-shot coordination (ZSC) addresses this bottleneck by simulating diverse partner populations to approximate how unseen partners might behave. However, partner coverage alone is insufficient as team settings scale and communication becomes degraded. To remedy this deficiency, we propose Influence-Based Team Steering (IBTS), a framework that uses influence shaping to incentivize agents to discover diverse, high-performing team interaction patterns and further steers ongoing trajectories toward stronger learned coordination modes. We assess IBTS on Overcooked-AI in both two-agent and three-agent settings, allowing us to test whether learned coordination structure transfers beyond dyadic interaction. 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