CLEARED TO MAINTAIN FL220. THOUGHT CLEARED TO FL230.

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RECEIVED CLRNC TO CLIMB FROM 17000' TO FL2300 FROM WASHINGTON CENTER CTLR. WE WERE THEN SWITCHED TO NEW SECTOR. UPON CHECKING IN I CALLED OUT OF 17500 FOR FL2300; THIS WAS ACKNOWLEDGED AND WE WERE SWITCHED AGAIN. THIS TIME I CALLED ABOUT TO LEAVE FL220 FOR FL2300. THE CTLR IMMEDIATELY SAID THAT WE WERE TO MAINTAIN FL220; AND THAT WE HAD TFC ONE O'CLOCK 7 MILES LEVEL FL2300. MY CO-PILOT IMMEDIATELY LEVELED OFF WITH A VERY SMALL (APPROX. 100') OVERSHOOT. I THEN RESPONDED THAT WE WERE LEVELED FL220 BUT THAT WE HAD READ BACK CLRNC TO FL2300. WE EVENTUALLY SPOTTED THE TFC WHO WAS INDEED AT FL2300. DURING THIS INCIDENT WE WERE FORTUNATE FOR SEVERAL THINGS. THE LAST CTLR MENTIONED; WAS NOT AS BUSY AS THE PREVIOUS TWO; THEREFORE; WE WERE ABLE TO MAKE OUR INITIAL CALL RIGHT AWAY; AND ALSO HE HAD THE CHANCE TO RECOGNIZE THE MISTAKE RIGHT AWAY. MY CO-PLT REACTED VERY QUICKLY TO LEVEL OFF IMMEDIATELY; ANY DELAY ON HIS PART WOULD HAVE MADE THIS A MAJOR CONFLICT. IN REVIEWING THE INCIDENT MY F/O AND I BOTH AGREED THAT WE WERE IN FACT CLRED TO FL2300 SINCE WE BOTH WERE AWARE OF INITIAL RECEIPT AND MY ACKNOWLEDGEMENT; AND ALSO MY CALL TO THE NEXT SECTOR INCLUDING THE ALT CLIMBING TO (FL230). IT CERTAINLY IS POSSIBLE THAT WE COULD HAVE BOTH BEEN IN ERROR; HOWEVER WE BOTH HAD 2 CHANCES TO CATCH AN ERROR. ON THE OTHER HAND THE FIRST TWO CTLR'S MENTIONED WERE SO BUSY THAT THEY HAD NO CHANCE WHATSOEVER TO HEARBACK MY ALTITUDE READBACK. MY OPINION IS THAT THE CTLR'S WORKING SEVERAL DIFFERENT FREQUENCIES AND/OR WORKING THESE POSITIONS ALONE CREATES THIS TYPE OF SITUATION. THE FIRST CTLR WAS WORKING ONE EXTREMELY BUSY FREQUENCY; APPARENTLY ALONE; AS HE WAS OFF ON THE HAND OFF LINE SEVERAL TIMES. IF WE HAD; IN FACT; MISSED THE CLRNC IT NORMALLY WOULD BE ON THE READBACK AND CERTAINLY BY THE NEXT CTLR.