Large language models (LLMs) have demonstrated remarkable performance in zero-shot dialogue state tracking (DST), reducing the need for task-specific training. However, conventional DST benchmarks primarily focus on structured user-agent conversations, failing to capture the complexities of real-world multi-user interactions. In this study, we assess the robustness of LLMs in multi-user DST while minimizing dataset construction costs. Inspired by recent advances in LLM-based data annotation, we extend an existing DST dataset by generating utterances of a second user based on speech act theory. Our methodology systematically incorporates a second user's utterances into conversations, enabling a controlled evaluation of LLMs in multi-user settings. Experimental results reveal a significant performance drop compared to single-user DST, highlighting the limitations of current LLMs in extracting and tracking dialogue states amidst multiple speakers. Our findings emphasize the need for future research to enhance LLMs for multi-user DST scenarios, paving the way for more realistic and robust DST models.