FLC OF ACR MLG ACFT EXPERIENCED DELAY IN LNDG DUE TO OTHER TFC CAUSING A GAR AND A LOSS OF LEGAL SEPARATION.

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SITUATION FIRST STARTED OUT NORMAL ON APCH TO DTW. TFC IN FRONT OF US ON THE APCH TO RWY 21L ILS WAS A GOOD 3 1/2 MI OR MORE IN FRONT AND VISUAL. TWR INSTRUCTED ACFT TO MAKE W-3 TURNOFF OR CONTINUE ALL THE WAY TO THE END AT W- 1 WHICH IS ALMOST 6000 FT FURTHER DOWN THE RWY. AS IT TURNED OUT; WE WERE INSTRUCTED TO GAR AFTER THE ACFT FAILED TO CLR IN TIME. THEN WE WERE INSTRUCTED TO CLB TO 4000 FT AND TURN TO 120 DEG HDG AND CALL DEP. EVENTUALLY WE WERE VECTORED INTO THE FLOW OF TFC FOR THE ILS (21L) AGAIN. WE HAD ALREADY DONE A LONG FINAL OF 20 MI OR MORE AT 170 KTS WITH SLATS AND FLAPS IN APCH CONFIGN; AND AGAIN DOING THE SAME ALL OVER AGAIN. AT THIS POINT WE DISCUSSED CALLING DISPATCH TO CHANGE OUR ALTERNATE TO YPSILANTI ARPT. BUT BEFORE WE COULD CALL; APCH HAD GIVEN US A HDG FOR THE BASE TURN TO ILS 21L. AS WE ROLLED OUT; WE NOTICED A TCASII ADVISORY THAT QUICKLY CHANGED TO AN RA TO DSND. SHORTLY AFTER INITIATING DSCNT; APCH ADVISED US TO TURN BECAUSE TFC HAD OVERSHOT THE FINAL; ALSO AT 4000 FT. WE HAD BRIEF VISUAL CONTACT WITH THE ACR MLG ACFT AND ADVISED ATC ACCORDINGLY. HE TOLD US TO MAINTAIN VISUAL WITH TFC. WE ADVISED THAT WE WOULD BE UNABLE. THIS WAS BECAUSE HE WAS REENTERING CLOUDS. THEN A SECOND RA WAS GIVEN AS WE HAD JUST GOTTEN A CLR OF CONFLICT; AND HAD STARTED A CLB BACK TO 4000 FT FROM ABOUT 3600 FT. THEN SECOND RA WAS MONITOR VERT SPD; MEANING DON'T CLB INTO THE RED. THERE WAS NO TARGET DISPLAYED ON THE IVSI/TCASII. FINALLY WE CLRED ALL THESE WARNINGS AND ATC HAD REGAINED CTL OF THE SITUATION. WE WERE CLRED FOR THE APCH AGAIN TO ILS 21L. AT THIS POINT WE DISCUSSED OUR PLANS IN THE EVENT OF A GAR AGAIN JUST IN CASE. OUR PLANS WERE TO DECLARE AN EMER OR MIN FUEL AS APPROPRIATE. AS THINGS WENT; THE TFC IN FRONT OF US MISSED THE TURNOFF AGAIN AND TWR ASKED US IF WE COULD ACCEPT 21C. WE DECLINED BECAUSE OF BEING CLOSE IN ON FINAL. HE THEN INSTRUCTED US TO GAR. I ELECTED TO ACCEPT THE RWY AS IT WAS CLOSE IN BUT ACCEPTABLE GIVEN THE CIRCUMSTANCES. THIS REQUIRED TURNS BELOW 500 FT AGL AGAINST COMPANY POLICY; BUT YET SAFE ENOUGH TO MAKE A NORMAL LNDG IN THE TOUCHDOWN ZONE. I LATER TRIED TO CALL ATC ON THE TELEPHONE TO DISCUSS THE SITUATIONS BUT NO ONE WAS ANSWERING. I CALLED DISPATCH AND EXPLAINED.