PBL,
Yes, good question!!!!
In the case of my company's incident that occurred several years ago, I honestly don't know the version of TCAS that was installed on our aircraft at that particular time. But, the TCAS system worked for the two conflicts. The second conflict occurred almost immediately after the first.
But, who knows what would happen if two or more conflicts occurred at exactly the same time...from two or more different directions...two or more different altitudes!!!!!
I guess, if that happens to you, you can definitely classify that as a 'bad day'!!!!
PantLoad