FLC OF A CPR EXECUTIVE JET CLBED IN RESPONSE TO ANOTHER SIMILAR SOUNDING CALL SIGN CLRNC. ATC INTERVENED AND INSTRUCTED THEM BACK TO THEIR ORIGINAL ASSIGNED ALT.

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WE WERE LEVEL AT 6000 FT. I WAS PIC WITH AUTOPLT ON. AS USUAL; THE FREQ WAS VERY BUSY. I WAS DISTRACTED WITH A NAV CHART I WAS REVIEWING AND DID NOT HEAR THE CLRNC TO 9000 FT. HOWEVER; I DEFINITELY DID HEAR THE SIC ACKNOWLEDGE A CLRNC TO 9000 FT -- 'ROGER NXX IS CLRED TO CLB AND MAINTAIN 9000 FT.' THE CTLR DID NOT CONFIRM OR CHALLENGE THE SIC'S READBACK (NOT UNUSUAL). THE SIC SET 9000 FT IN THE ALT ALERTER AND SAID TO ME; 'WE ARE CLRED TO 9000 FT.' ALTHOUGH I DID NOT HEAR THE CTLR CLRNC TO 9000 FT; NEITHER DID I HEAR HIM REJECT THE SIC'S CONFIRMING READBACK TO 9000 FT. SO; I WAS SATISFIED IT MUST BE CORRECT AND CLBED TO 9000 FT. APCHING 9000 FT; THE CTLR CALMLY ASKED WHAT OUR ALT WAS. SIC; 'WE ARE LEVELING AT 9000 FT.' CTLR; 'YOU WERE ONLY CLRED TO 6000 FT AND I GAVE YOU A NEW FREQ.' SIC; 'THAT'S NOT CORRECT SIR.' PIC (ME) I PULLED THE PWR ALL THE WAY BACK AND MADE A HIGH VERT SPD DSCNT BACK TOWARD 6000 FT. DURING THE DSCNT THE CTLR DID GIVE A NEW TRACON FREQ. THE NEW CTLR SAID 'OK; LET'S REVERSE IT AGAIN; YOU ARE NOW CLRED TO CLB AND MAINTAIN 11000 FT.' AFTER THE OCCURRENCE; NEITHER CTLR SAID ANYTHING ABOUT THE MATTER ONE WAY OR THE OTHER. WHILE CLBING TO 9000 FT AND BACK DOWN TO 6000 FT OUR TCASII SYS DID NOT INDICATE ANY TA OR RA ALERTS. THE SIC MAINTAINS HE HEARD A 9000 FT CLRNC. THERE WAS ANOTHER ACFT ON THE FREQ WITH A SIMILAR TAIL NUMBER. ON THE GND; WE CALLED NY TRACON TO ASK ABOUT THE INCIDENT. THE VOICE ON THE PHONE SAID; MAYBE YOU WERE CLRED TO 9000 FT OR MAYBE YOU WERE NOT. THE VOICE ON THE PHONE FURTHER STATED THAT THERE WERE NO TFC CONFLICTS AND SO THE MATTER WAS A NON ISSUE.