The widespread adoption of Large Language Models (LLMs) and LLM-powered agents in multi-user settings underscores the need for reliable, usable methods to accommodate diverse preferences and resolve conflicting directives. Drawing on conflict resolution theory, we introduce a user-centered workflow for multi-user personalization comprising three stages: Reflection, Analysis, and Feedback. We then present MAP -- a \textbf{M}ulti-\textbf{A}gent system for multi-user \textbf{P}ersonalization -- to operationalize this workflow. By delegating subtasks to specialized agents, MAP (1) retrieves and reflects on relevant user information, while enhancing reliability through agent-to-agent interactions, (2) provides detailed analysis for improved transparency and usability, and (3) integrates user feedback to iteratively refine results. Our user study findings (n=12) highlight MAP's effectiveness and usability for conflict resolution while emphasizing the importance of user involvement in resolution verification and failure management. This work highlights the potential of multi-agent systems to implement user-centered, multi-user personalization workflows and concludes by offering insights for personalization in multi-user contexts.