MLG CLBS ABOVE ASSIGNED ALT CAUSING CONFLICT.

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TOOK OFF AND HEADED NW. INITIAL CLB CLRNC TO 12000; RESTR TO 250 KTS. DEVIATED SLIGHTLY AROUND SMALL TSTMS IN VICINITY; GOT AND READ BACK NEXT CLRNC TO 'FL230; NORMAL SPD AFTER 180.' LEVELED FL230; GOT NEW CLB CLRNC TO 'FL290; TFC 3 O'CLOCK; 20 MI; FL270.' I READ BACK (ON FREQ 125.17) 'CLBING TO FL290; NOW RECEIVING TLH; REQUEST DIRECT.' CTLR RESPONDED; 'CLRED DIRECT' (AND I BELIEVE HE ALSO SAID CLB TO FL290). I THEN READ BACK; 'CLBING FL290; DIRECT TLH.' I SAW TFC AT APPROX SAME TIME AS TCASII ADVISORY 'TFC; TFC.' NO THREAT OF COLLISION AS BELOW AND MOVING ACROSS THE WINDSCREEN. ELECTED TO STAY ABOVE TFC; HOLDING APPROX 27600 FT AS TFC PASSED. CTLR IMMEDIATELY QUERIED ALT AND; UPON HEARING ME RPT 'THROUGH 27500 FOR FL290; TFC IN SIGHT;' ASKED WHERE WE GOT SUCH A CLRNC. CONFLICT RESOLVED; AND THEN ASKED AND LEVELED AT FL280. SUBSEQUENT CLB TO FL310; BACK ON RTING. AUTOPLT ALT ARMING/CLB PROCS ALL PERFORMED IN ACCORDANCE WITH FLT MANUAL; AND ALL SYS WORKED AS ADVERTISED. I BELIEVE THIS INCIDENT TO BE CAUSED BY INCORRECT CLB CLRNC FROM CTLR; AND THEN HE DIDN'T CATCH SUBSEQUENT READBACKS. THERE IS A POSSIBILITY OF CONFUSION DUE TO '6' VS '9;' OUR EARLY HDG OF '290 DEGS' WHILE DEVIATING AROUND WX; AND OUR CALL SIGN OF XXXX9. BOTH COCKPIT CREWMEMBERS BELIEVE FL290 WAS THE ALT CLRED TO.