NMAC BTWN A B737-200 DSNDING ON THE RWY 22 LOC FOR ILS AT 3200 FT AND A XING LIGHT TWIN NOT ISSUED AS TFC; 8 NM NE OF GSP; SC.

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ON APCH TO GSP; WE WERE ABOUT 500 FT BELOW THE CLOUDS WITH CLRNC TO INTERCEPT THE LOC (RWY 4). WE WERE AT 4000 FT; ABOUT 7-8 MI FROM THE RWY AND ABOVE THE GS. ATC CALLED TFC AHEAD AND BELOW US. THIS TFC (#2) WAS ON OUR TCASII AND APPARENTLY IT WAS THEIR PRESENCE THAT PROHIBITED THE CTLR FROM EITHER CLRING US FOR THE APCH OR ISSUING A DSCNT CLRNC ON THE LOC. ATC ASKED IF WE HAD VISUAL CONTACT WITH THAT ACFT AND COULD MAINTAIN. MY FO TOLD ME YES. I RELAYED SAME; AND ATC CLRED US TO 2600 FT WHILE MAINTAINING THIS TFC IN SIGHT. TCASII 'RA' OCCURRED FOR THIS #2 TFC. I NOTICED ADDITIONAL CONVERGING TFC (#3) AT 1 O'CLOCK POS; 300 FT ABOVE US (ON TCASII). THAT TFC TRIGGERED A TCASII RA AND ALMOST IMMEDIATE RA TO 'DSND NOW.' WE DSNDED IN ACCORD WITH THE RA; AND THE CLRNC TO 2600 FT. THE ACFT (#3) PASSED ALMOST DIRECTLY ABOVE US AT ABOUT 300-400 FT ABOVE US. ACFT #2 AND #3 WERE CLR OF CLOUDS; AS WERE WE. ADVISED ATC OF THE RA INVOLVING ACFT #3 AND THEY CLRED US FOR THE APCH. WAS QUITE THANKFUL OF THE TCASII; AND ALTHOUGH WE WERE COMPLETING A 13+ HR DAY; WE REACTED WELL TO A POTENTIALLY VERY HAZARDOUS OR DISASTROUS SIT. CONTRIBUTING FACTOR PERHAPS: ATC WORKLOAD IN GSP AREA WITH CONVECTIVE ACTIVITY IN THE AREA AND HIGH LEVEL OF TFC.