ACR ON ILS APCH TO RWY 32 AT PIT HAS A TCASII ENCOUNTER WITH 2 OTHER ACFT INBOUND FOR DIFFERENT RWYS.

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AFTER BEING CLRED FOR AN ILS APCH TO RWY 32 AT THE PIT ARPT; WE HAD TO INITIATE A GAR AT APPROX 2000 FT MSL. THE GAR AT APPROX 2000 FT MSL. THE GAR WAS INITIATED BECAUSE OF ANOTHER ACFT XING OUR APCH PATH WHILE ON A VISUAL FOR ANOTHER RWY. THE OTHER ACFT WAS APPROX 1 1/2 MI AHEAD AND AT OUR ALT. TCASII DID ISSUE AN ALERT. THE FLT CONDITIONS WERE VMC AT THE TIME. HOWEVER; THE OTHER ACFT WAS NOT RPTED TO US BY EITHER APCH CTL OR THE TWR CTLR. UPON INITIATING A TURN TO THE L BEHIND THE ACFT IN OUR WINDOW; WE QUESTIONED THE PITTSBURGH TWR ABOUT WHAT WE WERE OBSERVING IN FRONT OF US. THE TWR THEN GAVE US A TURN TO A HDG OF 270 DEGS. ONCE AGAIN WE WERE LOOKING AT ACFT LIGHTS HEADED IN OUR DIRECTION FROM ANOTHER ACFT. NO ALT WAS INITIALLY ASSIGNED BY THE TWR WITH THE TURN TO 270 DEGS UNTIL THE FO SUGGESTED 2500 FT; WHICH WE WERE RAPIDLY CLBING THROUGH. OUR CLB WAS ARRESTED AT 3500 FT AND THE ACFT DSNDED TO A NEW ASSIGNED ALT OF 3000 FT. WE WERE TURNED TO A DOWNWIND HDG FOR RWY 32 AND GIVEN A VISUAL APCH AND LNDG CLRNC TO RWY 32. A SAFE AND UNEVENTFUL LNDG WAS COMPLETED. LACK OF TIMELY INFO COMBINED WITH NIGHT VISUAL CONDITIONS AND GAR PROCS CREATED A HIGH WORKLOAD; CONFUSION; AND CONCERN WITHIN THE COCKPIT. HAD OUR FLT BEEN SLOWED WHILE FURTHER OUT ON THE APCH ALL CONCERN AND CONFUSION COULD AND WOULD HAVE BEEN ELIMINATED.