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Existing privacy-preserving inference methods sacrifice either utility or efficiency, and often require model-specific modifications that limit their compatibility. In this paper, we propose SharedRequest, a model-agnostic framework for privacy-preserving LLM inference that reformulates privacy protection at the batch level rather than the individual-prompt level. The key idea is to obscure sensitive information by mixing original prompts with noisy variants, while grouping semantically equivalent instructions to amortize the inference cost over a large batch of queries with minimal impact on LLM response quality. This design is independent of the LLM architecture, requiring no access to model parameters or architectural modification. 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