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This paper presents a physics-based method for creating complex multi-character motions from short single-character sequences. We represent multi-character motion synthesis as a spacetime optimization problem where constraints represent the desired character interactions. We extend standard spacetime optimization with a novel timewarp parameterization in order to jointly optimize the motion and the interaction constraints. In addition, we present an optimization algorithm based on block coordinate descent and continuations that can be used to solve large problems multiple characters usually generate. This framework allows us to synthesize multi-character motion drastically different from the input motion. Consequently, a small set of input motion dataset is sufficient to express a wide variety of multi-character motions.