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Metaphors are a crucial way for humans to express complex or subtle ideas by comparing one concept to another, often from a different domain. However, many large language models (LLMs) struggle to interpret and apply metaphors in multi-agent language games, hindering their ability to engage in covert communication and semantic evasion, which are crucial for strategic communication. To address this challenge, we introduce CoMet, a framework that enables LLM-based agents to engage in metaphor processing. CoMet combines a hypothesis-based metaphor reasoner with a metaphor generator that improves through self-reflection and knowledge integration. This enhances the agents’ ability to interpret and apply metaphors, improving the strategic and nuanced quality of their interactions. We evaluate CoMet on two multi-agent language games—Undercover and Adversarial Taboo—which emphasize “covert communication” and “semantic evasion”. Experimental results demonstrate that CoMet significantly enhances the agents’ ability to communicate strategically using metaphors.