ACR PLT DESCRIBED CONFLICT AT 4500 FT DURING VECTORS FOR ILS RWY 36L AT CLT.

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WE WERE SE OF THE ARPT BEING VECTORED FOR THE ILS RWY 36L. ACFT #2 WAS SW OF THE ARPT BEING VECTORED FOR THE ILS RWY 36R. WE GOT A 300 DEG HDG AND AN ALT OF 4000 FT. I READ BACK THE CLRNC. WE PUT 4000 FT IN THE ALT SELECTOR AND BOTH PLTS VERIFIED THE ALT. THIS IS WHEN WE BECAME AWARE OF THE OTHER ACFT. IT PASSED BELOW US AS WE WERE PASSING THROUGH 5000 FT. WE NEVER DID GET AN RA ON THE AIRPLANE BUT WE DID GET A TA. APCH CTL THEN TURNED US TO ABOUT 350 DEGS TO JOIN THE LOC AND TOLD US TO MAINTAIN 5000 FT TO MARJO CLRED FOR ILS RWY 36L. I TOLD APCH CTL YOU CLRED US TO 4000 FT. WE WILL HAVE TO CLB BACK UP TO 5000 FT. WE WERE ESTABLISHED ON THE LOC AND THE FO DID NOT START THE CLB TO 5000 FT UNTIL WE WERE AT 4100 FT AND I TOLD HIM TO DO SO. ONCE IN THE CLB; APCH CTL BROKE US OUT. L TURN 270 DEG HDG AND VECTORED US BACK AROUND FOR THE ILS TO RWY 36L. ACFT #2 WAS ESTABLISHED ON THE ILS FOR RWY 36R; BUT WAS CONCERNED ABOUT OUR ALT. COULD HAVE BEEN AVOIDED IF THE ACFT FROM THE W GOT VECTORED FOR THE ILS TO RWY 36L AND WE GOT THE ILS TO RWY 36R.