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In this paper, we develop an adaptive scheduling framework for changing the processor shares of tasks - a process called reweighting - on real-time multiprocessor platforms. Our particular focus is adaptive frameworks that are deployed in environments in which tasks may frequently require significant share changes. Prior work on enabling real-time adaptivity on multiprocessors has focused exclusively on scheduling algorithms that can enact needed adaptations. The algorithm proposed in this paper uses both feedback and optimization techniques to determine at runtime which adaptations are needed.