Depending on your point of reference as a threat...
"TCAS II was designed to operate in traffic densities of up to 0.3 aircraft per square nautical mile (nmi), i.e., 24 aircraft within a 5 nmi radius, which was the highest traffic density envisioned over the next 20 years."
FAA Intro to TCAS 2011
According to
Honeywell data:
"TCAS II can track as many as 45 aircraft, display up to 30 of them and can coordinate a resolution advisory for up to
three intruders at once. The advisories are always based on the least amount of deviation from the flight path while providing safe vertical separation" (emphasis added)