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Multimodal interfaces that combine direct manipulation and natural language have shown great promise for data visualization. Such multimodal interfaces allow people to stay in the flow of their visual exploration by leveraging the strengths of one modality to complement the weaknesses of another. In this work, we introduce an approach that interweaves multimodal interaction combining direct manipulation and natural language with flexible unit visualizations. We employ the proposed approach in a proof-of-concept system, DataBreeze. Coupling pen, touch, and s