FLC OF A LEAR JET OVERSHOT ALT DURING DSCNT AND FAILED TO TURN TO A NEWLY ASSIGNED HDG.

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THE PROB AROSE WHEN ZKC CLRED LEARJET TO FL240. THE FO READ BACK THE CLRNC AND SET FL240 IN THE ALT ALERT WINDOW. I STARTED THE DSCNT OUT OF THE LOW FL300 AT AROUND 52 NM FORM SUS ARPT; CTR ASKED IF X COULD MAKE A XING RESTR OF 5000 FT; 30 NM FROM SUS. I INSTRUCTED THE FO TO TELL ATC WE WERE UNABLE TO MAKE XING RESTR. A FEW MOMENTS ELAPSED AND I INSTRUCTED FO TO CONTACT ATC TO LET THEM KNOW WE WOULD TRY TO MAKE 5000 FT; 30 NM XING RESTR. THE FO TRIED SEVERAL TIMES TO CONTACT ATC; BUT RADIO FREQ CONGESTION HAD OCCURRED. AFTER FO ATTEMPTS; I RAISED THE MIKE AND TRIED TO CONTACT ATC MYSELF. AT SOME TIME DURING THE FREQ CONGESTION WE WERE GIVEN A R TURN TO A HDG OF 140 DEGS FROM AN ASSIGNED HDG OF 360 DEGS. (I LEARNED OF THE 140 DEG HDG CHANGE FROM MR X OF ZKC AFTER HE TELEPHONED ME ONCE I WAS ON THE GND AT SUS). THE FO MAY OR MAY NOT HAVE READ BACK THE HDG CHANGE; BUT I WAS UNAWARE OF THE NEW HDG ASSIGNMENT AND MAINTAINED A 360 DEG HDG. DURING THIS PERIOD; THE ACFT WAS DSNDING AS I WAS STILL TRYING TO CONTACT ATC TO INFORM THEM THAT WE WOULD CONTINUE DSCNT TO 5000 FT. WHEN I FINALLY RAISED ATC THE ACFT HAD DSNDED TO 22500 FT. I NOTICED THE ALT AND ASKED ATC IF WE WERE CLRED BELOW FL240; HIS REPLY WAS NEGATIVE YOU WERE CLRED TO FL240. THE CTLR REPLIED IMMEDIATELY AFTER THAT DSND AND MAINTAIN FL180 - OR - FL190 AND TURN 10 DEGS OR 20 DEGS L; I COMPLIED. SOON AFTER; WE WERE HANDED OFF TO ST LOUIS APCH. DSND AS CLRED BY ST LOUIS APCH TO BELOW 18000 FT AND CANCELED IFR. I BELIEVE THE REASON FOR THIS OCCURRENCE WAS: BREAK DOWN OF COM BTWN FLC. MISUNDERSTANDING OF ATC LAST CLRNC AND RADIO FREQ CONGESTION AT A CRUCIAL TIME. IN ORDER TO PREVENT A RECURRENCE; WE WILL PRACTICE BETTER COM AND CREW COORD; SO THIS MISUNDERSTANDING SHALL NOT HAPPEN AGAIN.