While personalisation in Human-Robot Interaction (HRI) has advanced significantly, most existing approaches focus on single-user adaptation, overlooking scenarios involving multiple stakeholders with potentially conflicting preferences. To address this, we propose the Multi-User Preferences Quantitative Bipolar Argumentation Framework (MUP-QBAF), a novel multi-user personalisation framework based on Quantitative Bipolar Argumentation Frameworks (QBAFs) that explicitly models and resolves multi-user preference conflicts. Unlike prior work in Argumentation Frameworks, which typically assumes static inputs, our approach is tailored to robotics: it incorporates both users' arguments and the robot's dynamic observations of the environment, allowing the system to adapt over time and respond to changing contexts. Preferences, both positive and negative, are represented as arguments whose strength is recalculated iteratively based on new information. The framework's properties and capabilities are presented and validated through a realistic case study, where an assistive robot mediates between the conflicting preferences of a caregiver and a care recipient during a frailty assessment task. This evaluation further includes a sensitivity analysis of argument base scores, demonstrating how preference outcomes can be shaped by user input and contextual observations. By offering a transparent, structured, and context-sensitive approach to resolving competing user preferences, this work advances the field of multi-user HRI. It provides a principled alternative to data-driven methods, enabling robots to navigate conflicts in real-world environments.