C550 FLT DEPART ASSIGNED ALT AFTER ASSUMING ZOB TRANSMISSION WAS FOR THEM.

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I FILED A FLT PLAN FROM GRR TO ILG. I FILED FOR FL330. RECEIVED MY CLRNC (MAINTAIN 4000 FT; EXPECT FL330 10 MINS AFTER DEP). STARTED OUT ON FLT AND WAS LEVELED SEVERAL TIMES PRIOR TO CRUISE ALT. AT THE TIME OF THE ALT BUST; I WAS JUST CHKING ON WITH THE NEXT CTLR AS 'CITATION WITH YOU CLBING TO FL250 (OR LEVEL FL250) -- I HONESTLY DON'T REMEMBER WHICH ONE IT WAS. ATC ANSWERED RIGHT AWAY SAYING 'ROGER; FL250' -- 1 OR 2 MIKE CLICKS FOLLOWED IMMEDIATELY BY 'CLB AND MAINTAIN FL330' (MY FILED; EXPECTED AND APPROPRIATE TIME FRAME FOR EXPECTING TO RECEIVE THOSE INSTRUCTIONS). I ANSWERED IMMEDIATELY; 'ROGER; CLB AND MAINTAIN FL330.' I RESET MY ALT ALERTER; CHKED MY TCASII AND INITIATED A 2000 FPM CLB TOWARDS FL330; PWR UP. THERE WAS NO OTHER ACFT I COULD HEAR RESPONDING TO THE CLRNC AND THE FREQ WAS QUIET. AT APPROX FL270; ATC CAME ON AND SAID 'I SHOW YOU CLBING THROUGH FL270; MAINTAIN FL270; YOU WERE ONLY CLRED TO FL250.' I LEVELED OFF AT FL270 AND SAID 'I THOUGHT YOU CLRED ME TO FL330.' THERE WAS NO ANSWER AND NO FURTHER DIALOG CONCERNING IT; BTWN ME AND THE CTLR. I WAS SWITCHED A SHORT TIME LATER TO THE NEXT CLEVELAND CTLR AND WENT ON WITH THE FLT. I THINK IT WAS A CLASSIC CASE OF 2 PLANES BLOCKING THE FREQ SIMULTANEOUSLY -- TWICE!