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Ride-pooling services, such as UberPool and Lyft Shared Saver, enable a single vehicle to serve multiple customers within one shared trip. Efficient path-planning algorithms are crucial for improving the performance of such systems. For partially occupied vehicles with available capacity, we introduce a novel routing algorithm designed to maximize the likelihood of picking up additional passengers while serving the current passengers to their destination. Unlike traditional methods that group passengers and vehicles based on predefined time windows, our algorithm allows for immediate responses to passenger requests. Our approach optimizes travel time while dynamically considering passenger demand and coordinating with other vehicles. Formulated as an integer linear programming (ILP) problem, our method is computationally efficient and suitable for real-time applications. Simulation results demonstrate that our proposed method can significantly enhance service quality.