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Recently, researchers have proposed various intersection management techniques that enable autonomous vehicles to cross the intersection without traffic lights or stop signs. In particular, a priority-based coordination system with provable collision-free and deadlock-free features has been presented. In this paper, we extend the priority-based approach to support legacy vehicles without compromising above-mentioned features. We make the hypothesis that legacy vehicles are able to keep a safe distance from their leading vehicles. Then we explore some special configurations of system that ensures the safe crossing of legacy vehicles. We implement the extended system in a realistic traffic simulator SUMO. Simulations are performed to demonstrate the safety of the system.