While Doppler radar measurement of respiration has shown promise for various healthcare applications, simultaneous sensing of respiration for multiple subjects in the radar field of view remains a significant challenge as reflections from the subjects are received as an interference pattern. Prior research has demonstrated the basic feasibility of using phase comparison with a 24-GHz Monopulse radar for isolation of one subject when another subject was in view, by estimating each subject's angular location with 88% accuracy. The integration of the high-resolution Multiple Signal Classification (MUSIC) algorithm with a phase-comparison technique is proposed to achieve robust accuracy for practical multi-subject respiration monitoring. Experimental results for this work demonstrate that the MUSIC pseudo-spectrum can separate two subjects 1.5 meters apart from each other at a distance of 3 meters from the sensor, using the same antenna array elements, spacing, and experimental scenarios previously reported for phase comparison Monopulse alone. Experimental results demonstrate that the MUSIC algorithm outperforms the phase-comparison technique with an azimuth angular position estimation accuracy over 95%. Higher accuracy indicates the system has improved robustness concerning noise and interference.