Efficient motion planning for high-dimensional robotic systems, such as manipulators and mobile manipulators, is critical for real-time operation and reliable deployment. Although advances in planning algorithms have enhanced scalability to high-dimensional state spaces, these improvements often come at the cost of generating unpredictable, inconsistent motions or requiring excessive computational resources and memory. In this work, we introduce Multi-Graph Search (MGS), a search-based motion planning algorithm that generalizes classical unidirectional and bidirectional search to a multi-graph setting. MGS maintains and incrementally expands multiple implicit graphs over the state space, focusing exploration on high-potential regions while allowing initially disconnected subgraphs to be merged through feasible transitions as the search progresses. We prove that MGS is complete and bounded-suboptimal, and empirically demonstrate its effectiveness on a range of manipulation and mobile manipulation tasks. Demonstrations, benchmarks and code are available at https://multi-graph-search.github.io/.