ACR X HAD LTSS FROM ACR Y WHILE ON RADAR VECTOR FOR SIMULTANEOUS ILS APCH.

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ACR X HAD CONFLICT WITH ACR Y. THIS OCCURRED WHILE BOTH ACFT WERE BEING VECTORED FOR SIMULTANEOUS ILS APCHS. ILS RWYS 18R/18L IN USE; WE WERE ON A HDG 120 DEGS FOR RWY 18R ILS (R BASE). WX CONDITION AT 4000 FT MSL WERE POOR. SCATTERED CLOUDS AND A CEILING BELOW US PREVENTED GND CONTACT. WHILE ON HDG 120 DEGS AT 4000 FT MSL; CREW NOTICED ANOTHER COMPANY 727 Y ON AN OPPOSING VECTOR FOR RWY 18L. (Y WAS APPROX 240 DEGS). Y WAS ABOVE OUR ALT; IT WAS OBVIOUS HE WAS DSNDING THROUGH OURS. APCH CTL POINTED OUT THE TFC AND I PURPOSELY DID NOT SAY THAT WE HAD 'TFC IN SIGHT.' APCH DID NOT APPEAR CONCERNED AS WE WERE VECTORED THROUGH OUR LOC DIRECTLY TOWARDS THE OTHER ACFT. CAPT INITIATED A GENTLE BANK N TO ENSURE SEPARATION; THEN BEGAN TURN TO S TO INTERCEPT LOC; WE ESTIMATE THAT Y PASSED 500 FT VERT AND 500 FT HORIZ AT NO TIME DID EITHER ACFT INDICATE THE OTHER WAS IN SIGHT. UPON INTERCEPT; I ASKED CTLR Y'S ALT; WE WERE AT 4000 FT THE OTHER AT 3200 FT. HAD THIS BEEN ACTUAL IMC AND PF HAD NOT TAKE CORRECTIVE ACTION; A COLLISION MAY HAVE RESULTED. IN THE FUTURE WE WILL BE MUCH MORE AGGRESSIVE WITH REGARD TO GETTING THE CTLR TO REACT. SUPPLEMENTAL INFO FROM ACN 298184: MEM APCH CALLED COMPANY TFC AT '11:00/3 MI.' ACR X LEVEL AT 4000 FT; IMC CONDITIONS. A BREAK IN THE CLOUDS ALLOWED A VISUAL WITH COMPANY TFC WHO WAS TRACKING THE LOC TO RWY 18L. WE WERE TOLD TO EXPECT THE ILS TO RWY 18R OUR HDG WAS 120 DEGS. WHEN I SAW THE TFC APPEARED TO BE DSNDING THROUGH OUR ALT; I MADE A 10 DEG L TURN IN ORDER TO ASSURE SOME LATERAL SEPARATION. THE ATC CTLR THEN GAVE US A HDG OF 220 DEGS TO INTERCEPT THE LOC TO RWY 18R. WE ASKED FOR COMPANY'S ALT AND WERE TOLD HE WAS AT 3200 FT MSL. WE HAD BEEN CLRED TO 3000 FT. THE REMAINDER OF THE FLT WAS UNEVENTFUL. HOWEVER; HAD WE CONTINUED TO REMAIN IN IMC CONDITIONS; A MIDAIR COULD HAVE OCCURRED.