BE30 CREW HAD ALTDEV IN ZKC CLASS A.

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WE WERE LEVEL FL230; ZKC ISSUED CLRNC PLT'S DISCRETION DSND TO 11000 FT FOR DSCNT TO FOE. I SET ALT ALERT TO 11000 FT AND CAPT CONFIRMED. DSCNT WAS DELAYED -- WE WERE BELOW VNAV PROFILE. INTERCEPTING THE VNAV PROFILE; CAPT ADVISED HE WAS READY TO DSND. I ADVISED ZKC WE WERE OUT OF FL230. I LOOKED DOWN AT CTR CONSOLE TO SET PRESSURIZATION FOR DSCNT. I NOTICED THE ALT ARM ANNUNCIATOR FLASHING ON THE CTR CONSOLE. I LOOKED UP AND SAW WE WERE CLBING THROUGH FL231. THE PLT'S AUTOPLT ANNUNCIATOR PANEL ALT ARM LIGHT WAS FLASHING AND THE CLB ANNUNCIATOR WAS ILLUMINATED. I TOLD THE CAPT HE HAD PUSHED THE CLB BUTTON AND WE WERE CLBING. RATHER THAN DISENGAGING THE AUTOPLT OR USING THE PITCH SYNC BUTTON TO STOP THE CLB; THE CAPT ATTEMPTED TO LOCATE THE APCH DSCNT BUTTON. THE ACFT CONTINUED TO CLB. I TOLD THE CAPT HE NEEDED TO DSND OR WE WOULD GET AN ALT ALERT; WHICH THE ACFT ALT ALERT WENT OFF. SUBSEQUENTLY THE ACFT CLBED TO FL234 BEFORE THE CLB WAS STOPPED AND A DSCNT WAS INITIATED. THERE WAS NO COMMENT FROM CTR QUESTIONING THE DEV. CLOSER MONITORING OF CAPT'S ACTIONS BY PNF AND MORE AGGRESSIVE AND POSITIVE ACTION BY THE CAPT ONCE THE ERROR WAS NOTICED WOULD HAVE ALLEVIATED THE SIT.