CORP ACFT MISHEARS CLRNC; CLBS ABOVE ASSIGNED ALT. LTSS.

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THE INITIAL CLB CLRNC WAS TO MAINTAIN 5000 FT. USUALLY WE ARE CLRED NEXT TO 10000 FT BUT TODAY'S SECOND ALT CLRED TO WAS 15000. THE NEXT ANTICIPATED ALT IS FL230. WHILE LEVEL AT 15000 FT WE HEARD THE CTLR CLR US TO FL220. THE FO READ BACK 'CLRED TO FL220.' DURING THE CLB WE WERE NOTIFIED OF TFC AT 10 O'CLOCK (APPROX -- I DON'T RECALL EXACT CLOCK POS AND DISTANCE). WE HAD VISUAL CONTACT WITH THAT ACFT. IT APPEARED TO ALSO BE A CORPORATE JET (WITH 2 ENGS). HIS CALL SIGN I BELIEVE TO BE 'EFM.' HE RPTED OUR ACFT 'IN SIGHT.' DURING THE SCENARIO I DID UNDERSTAND HIM TO BE AT FL210. HOWEVER; IT WAS NOT UNTIL HE PASSED IN FRONT OF US AND ABOVE US A FEW HUNDRED FT THAT I THOUGHT 'THIS IS PRETTY CLOSE PROX UNDER RADAR.' AS MY AIRPLANE WAS PASSING APPROX FL207 THE CTLR ASKED US TO CONFIRM LEVEL AT FL200. I GLANCED AT THE ALT SET GAUGE AND IT SAID 22000. THE FO SAID 'I READ BACK FL220.' WE WERE ABOVE FL210 BEFORE I STARTED A DSCNT TO FL200. PRIOR TO REACHING FL200 WE WERE RECLRED TO FL230. THEN WE WERE CLRED TO FL250 AND GIVEN A FREQ CHANGE. THE NEXT CTLR PASSED A MESSAGE AND A TELEPHONE NUMBER FOR ZID TO BE CALLED UPON LNDG. AT NO TIME PRIOR TO THE NEAR MISS DID I QUESTION THAT MY ASSIGNED ALT WAS FL220. REVIEWING IT IN MY MIND I CAN SEE THAT FL200 WAS THE RIGHT ALT FOR ASSIGNMENT AND IF THE TAPES PLAYED BACK CONFIRM IN ACTUALITY THAT ATC INDEED CLRED US TO FL200; I AM WONDERING HOW BOTH OF US MISSED HEARING IT CORRECTLY. SUPPLEMENTAL INFO FROM ACN 196126: I READ BACK EAM CLRED FL220. I REMEMBER THINKING FL220 WAS UNCOMMON. ZID ALERTED US WE HAD TFC AT 10-11 O'CLOCK AT FL210. THE CTLR THEN ASKED US TO VERIFY WE WERE LEVEL AT FL200. WE RESPONDED WE WERE AT FL207 CLBING TO FL220. HE SAID WE WERE ONLY CLRED TO FL200. I SAID I READ BACK FL220. WHILE THIS CONVERSATION WAS IN PROGRESS; THE PF WAS DSNDING TO FL200. WE HAD THE OTHER ACFT IN SIGHT. EVASIVE ACTION WAS NOT NECESSARY.