FLC OVERSHOT DSCNT ALT DUE TO DISTR CAUSING TFC CONFLICT AND ATC CTLR INTERVENTION BY GIVING AN EVASIVE TURN.

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PRIOR TO DSCNT AT FL370 WE WERE GIVEN INSTRUCTIONS OF INCREASE FORWARD SPD TO MAX POSSIBLE BECAUSE WE WERE #1 FOR ARR INTO STL. APPROX 30 MI NE OF SPG VOR ON TRAKE ARR AT MACH SPD .840 AND INCREASING WE WERE GIVEN A DSCNT CLRNC TO FL330. FO READ BACK CLRNC AND SET ALT INTO ALT ALERT. DURING DSCNT; THE FLT ATTENDANT ENTERED COCKPIT TO PICK UP AND DELIVER MEALS TO CREW. DUE TO HIGH AIR NOISE AND DISTR FROM FLT ATTENDANT IN THE FLC MISSED ALT ALERT AND DSNDED THROUGH 33000 FT. CAPT BECAME AWARE OF ALT AT 31500 FT AND NOTICE 33000 FT SET IN ALT ALERT. HE ASKED FO IF WE WERE CLRED TO 31000 FT ON 33000 FT? FO SAID 33000 FT. CAPT IMMEDIATELY BEGAN PULL UP ACFT REACHED 31000 FT AND BEGAN CLBING WHEN TCASII GAVE ALERT FOR IMMEDIATE CLB. AT SAME TIME ATC ASKED OUR HDG AND GAVE AN IMMEDIATE R TURN 90 DEGS TO WHICH WE COMPLIED IN BOTH DIRECTIONS; CLBING AND A R TURN. APPROX 30 DEGS INTO TURN AT 32000 FT TCASII ALERT FINISHED. ATC THEN GAVE US A CONTINUE TO DSND CLRNC TO 24000 FT. IN SUMMARY WITH A HIGH SPD AIR NOISE AND DISTR IN COCKPIT ALL 3 CREW MEMBERS MISSED LEVEL OFF ALT.