A B757-200 CREW ACKNOWLEDGED AN ALT ASSIGNMENT MEANT FOR ANOTHER ACR ACFT WITH A VERY SIMILAR SOUNDING CALL SIGN.

Narrative

TKOF FROM MIA. WE WERE LEVEL AT FL240 DEVIATING FOR WX W OF THE HEDLY TRANSITION. ATC WAS VERY BUSY. ATC XMISSION; 'ACR X CLB AND MAINTAIN FL340.' FO READ BACK CLRNC; 'ACR X FL340.' FO SET 34000 IN ALT WINDOW AND POINTED. I VISUALLY AND VERBALLY CONFIRMED 34000 IN THE WINDOW. I INITIATED A VNAV CLB. I CANNOT REMEMBER IF THE AUTOPLT WAS ENGAGED OR I WAS HAND FLYING. PASSING FL255 ATC XMISSION; 'ACR X LEVEL AT FL260; TFC AT 11 O'CLOCK POS 2-7-0.' FO READ BACK CLRNC AND SET 26000 IN ALT WINDOW AND POINTED. I VISUALLY AND VERBALLY CONFIRMED 26000 IN THE WINDOW. LEVEL AT FL260 ATC ASKED WHAT CLRNC WE HAD. THE FO COMMUNICATED THAT WE HAD CLRNC TO FL340 AND THAT HE HAD READ BACK THAT CLRNC TO CTR. ATC SAID THAT WE HAD TAKEN SOMEONE ELSE'S CLRNC. SEVERAL MINS LATER WE WERE CLRED TO FL380. AT XA45Z WE HEARD A XMISSION FROM CTR TO ACR Y TO SWITCH FREQS. NOT ONLY WERE THESE LIKE CALL SIGNS; THEY WERE NEARLY IDENTICAL. UNDER THESE CONDITIONS WITH A BUSY CTR; NUMEROUS DEVS AND GOOD BUT IMPERFECT XMISSIONS; EVEN THE STRICTEST FOLLOWING PROCS DID NOT PREVENT A POSSIBLE CALAMITY. THERE NEEDS TO BE SOME EFFORT MADE TO ELIMINATE LIKE OR IN THIS CASE NEARLY EXACT CALL SIGNS FROM BEING IN THE SAME AIRSPACE AT THE SAME TIME.