The recent development of high-fidelity U.S. airspace encounter models at Lincoln Laboratory has motivated a simulation study of the Traffic Alert and Collision Avoidance System (TCAS) multiple threat logic. We observed from archived radar data that while rarer than single-threat encounters, multiple threat encounters occur more frequently than originally expected. The multithreat logic has not been analyzed in the past using encounter models. To generate multi-threat encounters, this report extends the statistical techniques used to develop pairwise correlated encounters. We generated and simulated a large number of multi-threat encounters using the TCAS logic implemented in Lincoln Laboratory's Collision Avoidance System Safety Assessment Tool. Near mid-air collision (NMAC) count indicates how often close encounters are resolved, unresolved, or induced by TCAS. Change in vertical miss distance shows the effect of the additional threat on the vertical separation between the first two aircraft. Risk ratio measures how the probability of an NMAC changes when an aircraft is equipped with TCAS versus being unequipped. Study results indicate that in multi-threat encounters, the TCAS logic results in a more than twofold increase in unresolved NMACs and approximately five times more induced NMACs than one-on-one encounters. TCAS provides a safety benefit in multi-threat encounters by issuing resolution advisories that result in increased vertical separation between the equipped aircraft and the first intruder.