LTT ACCEPTS VISUAL BUT FOLLOWS WRONG ACFT WHEN TURNING BASE.

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WE WERE VECTORED FOR A R DOWNWIND AND SLOWED TO 210 KTS AT 6000 FT. THE CTLR WAS VERY BUSY; ON THE VERGE OF OVERLOAD; WITH SEVERAL ACFT COMPLAINING ABOUT MULTIPLE RWY CHANGES; RWYS 26 AND 27; MULTIPLE VECTORS; TURNS; AIRSPD CHANGES; ETC. THE WX WAS 2500 FT SCATTERED TO BROKEN WITH BUILDING CUMULUS CLOUDS THROUGH 6000 FT. THE WX PRECLUDED OUR SEEING ANY TFC AT 12 O'CLOCK. THE CTLR WITH NO WARNING OR EXPLANATION CALLED 'THE TFC YOU'RE FOLLOWING IS TURNING FINAL FOR RWY 26; A COMPANY MLG.' WE LOOKED AT OUR 3 O'CLOCK POS AND SAW AN MLG INBOUND FOR THE RWY. MY FO WITHOUT ASKING ME CALLED THE TFC IN SIGHT. THE CTLR THEN CLRED US 'FOLLOW THAT TFC CLRED FOR THE VISUAL RWY 26.' MY FO AGAIN ANSWERED WITHOUT CONSULTATION 'FOLLOW HIM; CLRED FOR THE VISUAL.' THIS TOOK ABOUT 4-5 SECONDS FROM THE INITIAL TFC CALL. I WAS CONCERNED ABOUT THE CLOUDS AND OUR ABILITY TO MAINTAIN THE VISUAL. MY FO ASSURED ME HE COULD KEEP THE TFC IN SIGHT ON HIS SIDE OF THE ACFT. DURING THIS THE RADIO CONTINUED AT A NONSTOP; OVERLOADED CLIP. I STARTED A DSCNT AND TURNED ONTO R BASE. WE WERE ABLE TO MAINTAIN VISUAL WITH THE MLG AT OUR 2-3 O'CLOCK POS. AT APPROX 4000 FT AND JUST PRIOR TO OUR TURN TO FINAL THE CTLR CALLED WITH A FRANTIC 'YOU FOLLOWED THE WRONG ACFT; TURN R HDG 270 DEGS AND CLB TO 5000 FT.' HE THEN CONTINUED HIS CONTINUOUS LITANY WITH OTHER ACFT. WE WERE UNABLE TO ANSWER HIM DUE TO RADIO CONGESTION. I IMMEDIATELY WENT TO MAX PWR AND ENTERED A 45 DEG BANK R TURN WITH A 20 DEG PITCH UP CLB SINCE ALL I KNEW WAS THERE WAS ANOTHER MLG HEADED TOWARD ME AT 9 O'CLOCK. MY FO SAW THE OTHER MLG ABOUT 1-2 MI AWAY ALSO ON BASE AS WE TURNED. THE CTLR TURNED US AGAIN TO 360 DEGS AND AGAIN DID NOT WAIT FOR AN ANSWER. I FEEL THIS WAS CAUSED BY IMPROPER CTLR PHRASEOLOGY AND PROCS; HVY TFC; CREW FATIGUE; 12TH LEG IN 27 HRS; AND A BREAKDOWN IN COCKPIT COMS.