With rising cardiovascular and respiratory disorders and an aging population, healthcare systems require efficient non-contact vital sign monitoring (NCVSM) solutions. This study introduces a robust framework for multi-person localization and vital signs monitoring using multiple-input-multiple-output (MIMO) frequency-modulated continuous wave (FMCW) radar in cluttered environments. First, we developed a hardware phantom that simulates multi-person NCVSM scenarios using recorded thoracic impedance signals to replicate cardiopulmonary dynamics, enabling repeatable validation under diverse conditions. Second, we designed a robust algorithm for multi-person localization leveraging sparse signal processing with physiological characteristics, alongside dictionary-based vital signs estimation that handles interfering respiration harmonics. An adaptive signal refinement procedure enhances continuous NCVSM accuracy by leveraging estimate continuity. Performance was validated through 12 phantom trials and 12 human trials in single- and multi-person scenarios, demonstrating superior performance. In multi-person human trials, our method achieved respiration rate accuracies of$94.14\%$,$98.12\%$, and$98.69\%$within error thresholds of 2, 3, and 4 breaths per minute, respectively, and heart rate accuracies of$87.10\%$,$94.12\%$, and$95.54\%$within the same thresholds, highlighting the framework's potential for reliable healthcare and IoT applications.