APCH CTLR VECTORING 2 COMPANY ACFT FOR ILS APCH TURNED SECOND ACFT ON ILS FIRST. SIMILAR SOUNDING A/N.

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ORD APCH CTL WAS RUNNING PARALLEL ILS APCHS TO RWYS 27L; 27R. OUR FLT WAS DOWNWIND; HDG 090 DEGS FOR VECTORS TO RWY 27L. WHEN APPROX 6 MI FROM ORD WE WERE GIVEN A TURN TO 360 DEGS. SHORTLY THEREAFTER ANOTHER ACFT WITH A SIMILAR SOUNDING FLT NUMBER WAS ISSUED A TURN TO 290 DEGS TO INTERCEPT THE 27L ILS. AT FIRST THOUGHT; SAID ACFT WAS THE ONE WE WERE FOLLOWING; BUT IT QUICKLY BECAME OBVIOUS THAT THE OTHER ACFT WAS ACTUALLY BEHIND US AND WAS NOW MISTAKENLY BEING PLACED AHEAD OF US. THE CREW OF THE OTHER ACFT KNEW OUR RELATIVE POS AND ATTEMPTED TO RESOLVE THE CONFLICT WITH ATC. WHEN ATC SAW WHAT THEY HAD DONE THEY ISSUED US VECTORS AND SPD CTL WHICH KEPT US SUFFICIENTLY SEPARATED TO CONTINUE THE APCHS ALBEIT IN REVERSE ORDER. IN REVIEWING THE EVENTS I BELIEVE THAT THERE WERE 2 PROBLEMS RESULTING FROM THE ATC MISHANDLING. THERE MAY HAVE BEEN A LOSS OF LEGAL SEPARATION. WE WERE UNABLE TO DETERMINE THAT WITH CERTAINTY DUE TO IMC CONDITIONS PREVAILING AT THE TIME. WE WENT THROUGH THE 27L ILS COURSE AND WERE INFRINGING UPON THE TFC FOR RWY 27R OR PARALLEL APCHS. HOWEVER AT THAT POINT; THERE IS NORMALLY A 1000 FT VERT SEPARATION TO PROTECT AGAINST ANY OVERSHOOTS.