MULTIPLE RWY CHANGES OVERBURDENS A B757 FLC WHO FAIL TO IDENT THE NEWEST ILS FREQ. THE RESULTING WRONG RWY APCH CREATES A POTENTIAL CONFLICT.

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LOCATION: 8 MI S OF RWY 35C. I WAS PF; AND WE WERE ON THE BOWIE 1 ARR. WX WAS 500 FT 1 MI WITH BLOWING SNOW. INITIAL APCH CTLR TOLD US TO EXPECT RWY 36L. WE HAD SET UP FOR THAT AND BRIEFED IT. WE TURNED DOWNWIND SHORT OF SILER; AND NEXT APCH CTLR ASSIGNED US RWY 36L -- SO FAR; SO GOOD. HE THEN CHANGED US TO RWY 35R. CAPT REPROGRAMMED THE FMS; NAVAIDS AND WE BRIEFED THE APCH. JUST PRIOR TO TURNING BASE; WE WERE GIVEN A THIRD RWY CHANGE; TO RWY 35C; FOLLOWED SHORTLY BY TURN TO DOGLEG FINAL AND CLRNC FOR THE APCH. IN OUR HASTE TO COMPLY; WE MISSED CHKING THE NAVAID FREQ; AND OVERSHOT FINAL. SPD CHANGE AND FREQ CHANGE TO TWR. TO COMPLICATE; WE WERE WATCHING AN ACFT ON BASE FROM THE E; WHO TURNED FINAL IN FRONT OF US. IN THE CONFUSION; BOTH CAPT AND I NEGLECTED TO DOUBLECHK THE NAVAID; WHICH WAS STILL ON RWY 35R. WHEN WE ROLLED OUT; BOTH THE CAPT AND I SAW THE ACFT IN FRONT OF AND BELOW US. ESTIMATE CLOSEST DISTANCE AS 1 MI WITH 500 FT ALT DIFFERENCE. ALMOST SIMULTANEOUSLY THE TWR CTLR TOLD US TO LEVEL OFF AND CHK LOC FREQ. WE DID AND LANDED UNEVENTFULLY AFTER THAT. BOTH OF US ERRED IN NOT CHKING THE NAVAID; BUT WE WERE VERY DISTR BY HAVING HAD THE LNDG RWY CHANGED 3 TIMES IN HVY IMC. SUPPLEMENTAL INFO FROM ACN 357897: WHILE CHANGING APCH CTL FREQS AND COMPLETING OUR OTHER APCH WE ENTERED AN INCORRECT FREQ FOR THE ILS RWY 35C; AND THUS OVERSHOT THE LOC FOR RWY 35C AND CAME FAIRLY CLOSE TO ANOTHER ACFT THAT WAS ON THE APCH TO RWY 35R. IN SUMMARY; I FEEL THAT 3 APCH CHANGES IN MARGINAL WX IS NOT A GOOD IDEA.