CPR MDT ALT DEVIATION EXCURSION FROM CLRNC ALT IN REPLY TO WRONG CALL SIGN.

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ACFT DEPARTED TOL EXP ARPT ON A FLT TO JAX; FL. DEP RECLRED OUR FLT TO CONTINUE CLBING TO 8000' AND MAINTAIN HDG 210. PASSING THROUGH 6500' DEP RECLRED OUR FLT TO FL230. CLBING THROUGH 12500' DEP SWITCHED US TO CLE CENTER. CHKED IN WITH CLR LEAVING 13500' CLBING TO FL230 AND HDG 210. ACFT LEVELED AT FL230 AT ABOUT 5 MINS AFTER TKOF AND I ADVISED CENTER OF OUR LEVEL OFF. AT THIS TIME CENTER GAVE OUR FLT A COURSE CHANGE OF DIRECT APE AND CLB TO FL250. WE ACKNOWLEDGED THIS CLRNC WITH THE NORMAL READ BACK AND RECEIVED THEIR ACKNOWLEDGEMENT. CLE CENTER THEN GAVE A CLB CLRNC TO FL270 AND SWITCHED US TO IND CENTER. I MADE THE NORMAL CALL INTO IND AND CHKED LEVELING AT FL270. THEY ACKNOWLEDGED OUR FLT. (LOTS OF TFC ON FREQ.) ABOUT A MINUTE AFTER OUR CALL IN; IND CALLED WITH CLRNC FOR XXX TO CLB TO FL290. I ACKNOWLEDGED THIS CLRNC AND RECEIVED HIS CONFIRMATION. WE STARTED CLBING TO THE NEWLY ASSIGNED ALT. WHEN APCHING FL278 I HEARD THE CTLR GIVE ANOTHER ACFT WITH SIMILAR SOUNDING CALL SIGN (XXX AB) A CLB CLRNC TO FL290. AT THIS TIME WE STOPPED OUR CLB AND STARTED DSNDING BACK TO FL270 ALONG WITH CONVERSING WITH CENTER ABOUT OUR POSSIBLE INADVERTENT ACCEPTANCE OF ANOTHER ACFT'S CLRNC. THE CTLR SAID HE NEVER HEARD OUR ACKNOWLEDGEMENT OR READBACK OF THE CLRNC. OUR FLT RELEVELED AT FL270 AND CONTINUED ON OUR WAY WITH NO OTHER COMMENTS BY EITHER PARTY. S OF APE VOR OUR FLT WAS SWITCHED TO ANOTHER SECTOR. TWO MINS AFTER OUR RELEVEL AN AIRLINE LGT PASSED AT 12 O'CLOCK AND 1 MI AND FL280 (?). THIS INADVERTENT ACCEPTANCE OF ANOTHER ACFT'S CLRNC OCCURRED BECAUSE OF THE FOLLOWING: A) OUR FLT HAD RECEIVED 3 PREVIOUS STEP CLB CLRNCS. B) WE WERE STANDING BY AND READY FOR ANOTHER WHICH I THOUGHT I'D HEARD. C) CTLR WAS HANDLING A MULTITUDE OF ACFT TRANSGRESSING HIS SECTOR. D) HIGH WORK LOAD FOR ALL PARTIES INVOLVED.