The paper proposes a multi-body electromagnetic (EM) model for the quantitative evaluation of the influence of multiple human bodies in the surroundings of a radio link. Modeling of human-induced fading is the key element for the development of real-time Device-Free (or passive) Localization (DFL) and body occupancy tracking systems based on the processing of the Received Signal Strength (RSS) data recorded by radio-frequency devices. The proposed physical-statistical model, is able to relate the RSS measurements to the position, size, orientation, and random movements of people located in the link area. This novel EM model is thus instrumental for crowd sensing, occupancy estimation and people counting applications for indoor and outdoor scenarios. The paper presents the complete framework for the generic N-body scenario where the proposed EM model is based on the knife-edge approach that is generalized here for multiple targets. The EM-equivalent size of each target is then optimized to reproduce the body-induced alterations of the free space radio propagation. The predicted results are then compared against the full EM simulations obtained with a commercially available simulator. Finally, experiments are carried out to confirm the validity the proposed model using IEEE 802.15.4-compliant industrial radio devices.