FO OF A B737-400 OVERSHOT DSCNT TRANSITION FOR APCH ALT DUE TO DISTR OF RWY ASSIGNMENT CHANGES AND THE FLT DIRECTOR NOT PROVIDING LEVELOFF GUIDANCE.

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WE WERE ASSIGNED RWY 36L IN CLT ON OUR FIRST COM WITH CLT APCH. ATC (CLT APCH) HAD CLRED US TO DSND TO 3600 FT AND SIMULTANEOUSLY GAVE US RWY 36R. I WAS MANUALLY FLYING THE ARR WITH FLT DIRECTOR GUIDANCE AND AUTOTHROTTLES ENGAGED. THE CAPT AND I BOTH POINTED TO '3600' IN THE ALT ALERT WINDOW AND HE WENT TO HIS COMMERCIAL CHART BINDER TO FIND THE NEW APCH PLATE. THE CAPT SET MY RADIOS AND COURSE SELECTOR TO THE NEW RWY AND STARTED TO BRIEF THE NEW APCH WHEN ATC CALLED TO SWITCH US TO THE FINAL CTLR. WE SWITCHED FREQS AND ATC ADVISED US TO EXPECT RWY 36L. WITH THIS THIRD RWY CHANGE; THE CAPT QUESTIONED ATC WHILE HE RETURNED MY RADIO TO THE RWY 36L FREQ. THE APCH CTLR QUICKLY CORRECTED HIMSELF AND WE RESET THE RADIOS (AGAIN) TO THE PROPER FREQ FOR RWY 36R. DURING ALL OF THIS; I (AS THE PF) CALLED OUT ' FOUR THOUSAND SIX HUNDRED FOR THREE THOUSAND SIX HUNDRED' AND CONTINUED TO DSND FOLLOWING FLT DIRECTOR COMMANDS. THE NEXT THING I KNEW; THE ALT ALERT AURAL WARNING SOUNDED AND THE ALT LIGHT WAS FLASHING. WE WERE DSNDING THROUGH 3400 FT. I IMMEDIATELY ADDED PWR AND RETURNED TO 3600 FT. THE FLT DIRECTOR COMMAND BARS HAD NEVER COMMANDED 'FLY UP' FOR THE LEVELOFF; THE AUTOTHROTTLES NEVER ADVANCED; AND I WAS SO WRAPPED UP IN ALL OF THE RWY CHANGES THAT I FAILED TO NOTICE THAT WE WERE DSNDING BELOW OUR ASSIGNED ALT. THE CTLR'S ONLY COMMENT WAS TO ASK US OUR TYPE ACFT (IE; 'ACR X SAY YOUR TYPE ACFT?'). ERROR MGMNT: 1) AS SOON AS WE GOT THE FIRST RWY CHANGE FROM CLT APCH; I SHOULD HAVE SELECTED THE AUTOPLT 'ON' ONCE AGAIN TO ADD A BARRIER TO ERROR. BY HAND FLYING THE ACFT; MY ATTN WAS DIVIDED BTWN FLYING THE AIRPLANE AND TRYING TO UNDERSTAND ALL OF THE RWY CHANGES THAT WERE ASSIGNED. THE CAPT WAS NO HELP BECAUSE HE WAS IN HIS APCH BOOK CONTINUOUSLY PULLING OUT NEW APCH PLATES; BRIEFING; AND SETTING UP RADIOS FOR ME. HAD THE AUTOPLT BEEN ON; PERHAPS I WOULD HAVE CAUGHT AN ALTDEV QUICKER -- IF IT HAPPENED AT ALL. 2) MECHANICAL MALFUNCTION. FOR SOME REASON THE FLT DIRECTOR FAILED TO COMMAND 'FLY UP.' I DON'T KNOW WHY THAT OCCURRED; BUT IT IS NO EXCUSE. AS PF; I SHOULD HAVE BEEN AWARE THAT WE WERE DEVIATING FROM OUR CLRNC. EVEN THOUGH I CALLED 'FOUR THOUSAND SIX HUNDRED FOR THREE THOUSAND SIX HUNDRED;' IN THAT SHORT THOUSAND FT SPAN OF TIME I BECAME DISTR. 3) THE FIRST LESSON THAT EVERY STUDENT LEARNS IS 'AVIATE; NAV; COMMUNICATE.' I SHOULD HAVE CONTINUED TO FLY THE AIRPLANE FIRST AND FOREMOST AND LET THE CAPT CONCENTRATE ON DEALING WITH ATC AND THE RAPID-FIRE CHANGES. 4) ATC CTLRS NEED TO UNDERSTAND THAT; ESPECIALLY TODAY IN THE ENVIRONMENT OF STRICT CRM COMPLIANCE; RWY CHANGES ARE TIME CONSUMING AT BEST. WE NEED TO SET UP RADIOS; CDI'S; MINIMUM ALT BUGS; SPD BUGS; PROGRAM THE FMC AND BRIEF THE APCH TO EACH OTHER. WHILE LAST MIN RWY CHANGES MAY HAVE BEEN APPROPRIATE 30 YRS AGO; TODAY THEY ARE NOT! (I CAN THINK OF A FEW ARPTS THAT DON'T EVEN ASSIGN A RWY UNTIL YOU'RE WITHIN 15 OR SO MI OF THE ARPT. THIS IS UNACCEPTABLE. RWY ASSIGNMENTS SHOULD BE GIVEN AS EARLY AS POSSIBLE.) IF WE AS A CREW ARE FALLING BEHIND; THEN IT IS OUR RESPONSIBILITY TO REQUEST DELAY VECTORS UNTIL WE CAN GET CAUGHT UP.