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)?

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)?

Let's assume a situation in which ATC suffers a catastrophic failure and is removed from the picture for some time (for example a major malfunction, foul play, or similar).

In this scenario, I assume it would take some time for contingency processes to kick in (for example alternative comms, etc), and in the meanwhile only TCAS would separate the traffic

If we are in a high-density environment, how likely is it for TCAS to become overwhelmed in such a scenario? That is, receiving multiple conflicting traffic alerts where the attempt to resolve one would lead to creating another?

Are there any actual examples of something like this ever happening?

EDIT: I would like to clarify my question a bit, to also better differentiate it from the post of which my question is considered duplicate.

I understand that TCAS can handle several "targets" simultaneously. However, I'm interested in the (perhaps highly hypothetical) scenario where TCAS would need to deal with multiple targets (more than 3-4) in a dense environment - say, near a busy aerodrome. 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)

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)?