I understand that TCAS can handle several "targets" simultaneously. However, I'm interested in the (highly hypothetical) scenario where TCAS would need to deal with multiple conflicts in a dense environment.

Is there a point where TCAS goes into some sort of "cannot resolve" mode becoming effectively inoperable, or does it try to cope with everything thrown at it, even if it leads to impossible solutions (defined here as maneuvers outside the flight envelope or the ability of crews to follow in a timely manner)?