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We address the largely unexplored problem of designing a batch of experiments that each simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of a budget-constrained batch of experiments. By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms. 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