Multi-person global human mesh recovery (HMR) is crucial for understanding crowd dynamics and interactions. Traditional vision-based HMR methods sometimes face limitations in real-world scenarios due to mutual occlusions, insufficient lighting, and privacy concerns. Human-floor tactile interactions offer an occlusion-free and privacy-friendly alternative for capturing human motion. Existing research indicates that pressure signals acquired from tactile mats can effectively estimate human pose in single-person scenarios. However, when multiple individuals walk randomly on the mat simultaneously, how to distinguish intermingled pressure signals generated by different persons and subsequently acquire individual temporal pressure data remains a pending challenge for extending pressure-based HMR to the multi-person situation. In this paper, we present \textbf{PressTrack-HMR}, a top-down pipeline that recovers multi-person global human meshes solely from pressure signals. This pipeline leverages a tracking-by-detection strategy to first identify and segment each individual's pressure signal from the raw pressure data, and subsequently performs HMR for each extracted individual signal. Furthermore, we build a multi-person interaction pressure dataset \textbf{MIP}, which facilitates further research into pressure-based human motion analysis in multi-person scenarios. Experimental results demonstrate that our method excels in multi-person HMR using pressure data, with 89.2 $mm$ MPJPE and 112.6 $mm$ WA-MPJPE$_{100}$, and these showcase the potential of tactile mats for ubiquitous, privacy-preserving multi-person action recognition. Our dataset & code are available at https://github.com/Jiayue-Yuan/PressTrack-HMR.