AN AIR TAXI FREIGHT JET OVERSHOT CLRNC ALT. THE CAPT CITED AUTOPLT AND MODE C MALFUNCTIONS AS FACTORS.

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THE INCIDENT OCCURRED COMPLETING THE LAST LEG OF OUR SCK- DEN-LAS-SCK TRIP. BOTH PLTS WERE QUITE TIRED AS OUR SCK DEP WAS AT XO37 AM AND IT WAS NOW CLOSE TO XA00 AM. DEPARTING LAS ARPT ON THE OASIS 8 DEP/BEATTY TRANSITION; ZLA CLRED US TO FL350. THE ACFT WAS LIGHT AND WAS CLBING THROUGH APPROX FL260 AT 2000-3000 FPM WHEN ZLA INSTRUCTED US TO CLB AND MAINTAIN FL280 DUE TO TFC: A B737 WAS AT 12 O'CLOCK AT FL290. I ACKNOWLEDGED THE NEW ALT ASSIGNMENT; DIALED 28000 FT INTO THE ALT ALERTER; POINTED TO IT; AND RECEIVED ACKNOWLEDGEMENT FROM THE PF THAT FL280 WAS THE NEWLY ASSIGNED ALT. I PROCEEDED TO LOOK FOR TFC; AND WITHIN SECONDS OF SETTING THE ALT ALERTER; IT SOUNDED; SIGNALING PASSING THROUGH 27000 FT. THE PF RAISED HIS FINGER TO SIGNIFY THAT WE HAD 1000 FT LEFT TO CLB TO OUR ASSIGNED ALT. THE PF BEGAN TO REDUCE HIS RATE OF CLB PASSING THROUGH 27500 FT AND IT APPEARED THAT A LEVEL OFF WAS IN PROGRESS. I MOVED MY ATTN TO LOOKING FOR THE B737 AND SECONDS LATER THE ALT ALERTER WENT OFF; SIGNALING THAT THE ACFT WAS AT 28300 FT. I LOOKED AT THE ALTIMETER AS THE PF PUSHED THE ACFT BACK DOWN TO 28000 FT. THE HIGHEST ALT THAT I NOTICED WAS 28380 FT. THE B737 PLT COMPLAINED TO ZLA THAT THEY HAD RECEIVED A TCASII ALERT AND HAD INITIATED EVASIVE ACTION. ZLA ASKED US IF THE INSTRUCTION TO CLB AND MAINTAIN FL280 WAS ACKNOWLEDGED; I RESPONDED THAT IT WAS. THE B737 PLT CONTINUED TO COMPLAIN AND ASKED HOW FAR OFF OUR ALT WAS; ZLA RESPONDED THAT OUR ALT WAS OFF BY 400 FT. ZLA THEN ASKED US TO CALL THEIR NUMBER REGARDING A POSSIBLE PLT VIOLATION. AFTER WE LANDED THE PF CALLED THE CTR. SUPPLEMENTAL INFO FROM ACN 313028: ON A PART 91 REPOSITION FLT; MY COPLT AND I HAD JUST RECENTLY LEVELED OFF AT FL280 AND ENGAGED THE AUTOPLT. EVERYTHING LOOKED NORMAL AND OPERATING CORRECTLY. SHORTLY AFTER; AN AIRLINER RPTED A TCASII RA TO CLB AND MADE AN INQUIRY TO ATC. ATC RPTED 'YEAH; THE LEAR BUSTED HIS ASSIGNED ALT.' NOTHING MORE WAS DISCUSSED ON FREQ. ACFT HAD PREVIOUSLY HAD MODE C PROBS; SO I ASKED THE NEXT CTR FOR A VERIFICATION OF ALT; AND THIS TIME ATC RPTED US 200 FT LOW. MODE C WAS WRITTEN UP ON RETURN TO BASE.