A B747F FLC WAS CLBING THROUGH FL320 AND CAME WITHIN 1000 FT VERT AND 6000 FT HORIZ NEAR STM; FO.

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WHILE FLYING A TRIP FROM MIA-TTPP-SBKP; AFTER MAKING MY POS RPT AT STM; FL290; I REQUESTED CLB CLRNC TO FL330 FROM BELEM CTL ON HF. BELEM CTL CLRED US TO CLB TO FL330 'RPT REACHING.' OUT OF FL320 WE OBSERVED AN ACR Y DC10 CRUISING OPPOSITE DIRECTION AT WHAT I BELIEVE WAS FL310. WE WERE MAKING OUR REQUIRED IATA POS RPT ON VHF 126.95 AND MONITORING VHF 130.55 AND VHF 121.5; BUT WE ONLY HEARD ONE OTHER ACFT MAKING RPTS (NOT ACR Y) ON ANOTHER AIRWAY. THERE WASN'T A CONFLICT BUT THERE COULD HAVE BEEN IF WE WERE CLBING A LITTLE SLOWER OR STARTED ANY LATER. WE WERE FLYING A B747 FREIGHTER THAT HAD BEEN CONVERTED FROM PAX CONFIGN THAT HAD A TCASII INSTALLED AT ONE TIME. I THINK IT'S CRIMINAL THAT THE FAA ALLOWS COMPANIES TO REMOVE A SAFETY SYS LIKE THE TCASII FROM ACFT JUST BECAUSE THEY DON'T CARRY PAX (6 CREW MEMBERS ON OURS). SOUTH AMERICA IS DANGEROUS ENOUGH AND WHILE FLYING AROUND WITH ATC; HIGH TERRAIN; LANGUAGE BARRIERS; INCREASING TFC VOLUME; AND THE LACK OF ENTHUSIASM IN WHICH MANY PLTS REGARD THE MANDATORY IATA POS RPTS; IT'S ONLY GOING TO COST SOMEBODY DEARLY IN THE FUTURE. I FIRMLY BELIEVE TCASII SHOULD BE REQUIRED HARDWARE ON ALL ACFT FLYING JET RTES.