FLC OF AN MLG OVERSHOT ALT DUE TO DISTR IN COORDINATING WX DIVERT WITH COMPANY.

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AT INITIAL CONTACT WITH FT WORTH CTR; WE WERE CLRED FROM 17000 FT TO FL250. WE HAD JUST DEPARTED A WX HOLDING PATTERN OVER AMARILLO VOR AND WERE RETURNING TO DFW. AUTOPLT AND AUTOTHROTTLES WERE PREVIOUSLY ENGAGED. AS THE PNF; I SET THE ALT WINDOW TO FL250 AND THE CAPT ACKNOWLEDGED '250.' I THEN GOT BUSY WORKING ON THE DIVERT AND SETTING UP FOR THE SHORT LEG TO DFW. I GLANCED AT THE ALTIMETER AS WE WERE APCHING FL250 AND CALLED 'ALT!' TO THE PLT. HE IMMEDIATELY DISCONNECTED THE AUTOPLT AND PUSHED THE NOSE OVER. THE ALTIMETER REACHED FL255 BEFORE STARTING DOWN. COINCIDENT WITH RETURNING TO LEVEL FLT AT FL250 THE CTLR ASKED 'SAY ALT?' AND WE RESPONDED FL250. AS WE LEVELED OFF; I NOTED THAT THE ALT SET WINDOW WAS SET AT FL200 INSTEAD OF FL250. CONTRIBUTING FACTORS WERE AN EXTREMELY BUSY DIVERT; 3 FAST RADIO CHANGES IN THE CLB; ICING; TURB; IMC AND NIGHT. WE HAD BEEN ON APCH TO AMARILLO. WHEN IT WAS BROKEN OFF AND WE WERE GIVEN HOLDING INSTRUCTIONS. WE HELD UNTIL WE HIT 'BINGO' FUEL FOR DFW. WE REQUESTED CLRNC TO DFW. AMARILLO APCH GAVE US AN INITIAL CLB AND VECTOR AND HANDED US OVER TO ZAB WHO CLBED US TO 17000 FT AND TURNED US OVER TO ZFW. HUMAN FACTORS: THE CAPT WAS TRYING TO COORD WITH COMPANY DISPATCH WHILE CLBING OUT. DISPATCH INSTRUCTED HIM TO RETURN TO AMARILLO; SHOOT THE APCH AND IF UNABLE TO LAND TO DIVERT LUBBOCK. I WAS HEARING BITS OF THE CONVERSATION AND TRYING TO SIMULTANEOUSLY PREPARE FOR ALL CONTINGENCIES. BOTTOM LINE: 1 PLT SHOULD HAVE BEEN STRICTLY FLYING THE ACFT AND TALKING TO CTR WHILE THE OTHER PLT COORDINATED WITH COMPANY. I DON'T KNOW HOW THE ALT SET GOT FROM 250 TO 200 AND WHY WE DIDN'T GET A WARNING WHEN THE ACFT CLBED ABOVE FL200. CORRECTIVE ACTION: 1 PLT SHOULD BE SOLELY INVOLVED IN FLYING OR MONITORING THE ACFT PERFORMANCE.