Services provided by mobile edge clouds offer low-latency responses for large-scale and real-time applications. Dynamic service management algorithms generate live service migration requests to support user mobility and ensure service latency in mobile edge clouds. To handle these migration requests, multiple migration planning and scheduling algorithms are necessary to calculate the migration order and optimize the performance and overhead of multiple migrations. However, current planning and scheduling algorithms in cloud data centers are not suitable for dynamic and large-scale scenarios in edge computing, as the network topology expands and the number of migration requests increases. Edge computing requires near real-time scheduling to handle user mobility-induced live migrations. To address this issue, this paper presents an efficient multiple migration planning and scheduling framework for edge computing. The framework includes a lifecycle management framework and innovative iterative Maximal Independent Set-based scheduling algorithms based on the resource dependency graph of multiple migrations. Our solution is shown to efficiently schedule live migrations at scale using real-world taxi traces and telecom base station coordinates. It can achieve significant processing speedups over existing migration planning algorithms in clouds, up to 3000 times, while ensuring multiple and individual migration performance for time-critical services.