EMJ CREW ON 3 MI FINAL SPOT A PA28 1 MI AHEAD LINING UP WITH RWY 32R INSTEAD OF RWY 32L AT CMI. A HIGH CLOSURE RATE CAUSED THE CREW TO TAKE EVASIVE ACTION.

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UPON CONTACTING APCH; WE WERE ADVISED THAT WE WERE #6 BEHIND 5 PIPER SINGLE ENG AFT AND ASKED TO SLOW TO 150 KTS. SHORTLY AFTER; APCH CHANGED OUR SEQUENCE TO #3 AND VECTORED US TO FINAL. CONTACTED TWR JUST OUTSIDE VEALS OM ON A VISUAL APCH. TOLD TO CONTINUE AND THAT WE WERE #3 BEHIND ONE ON THE RWY AND ONE ON SHORT FINAL. SEVERAL SECONDS LATER; WE WERE CLRED TO LAND WITH ONE ROLLING OUT AND ONE SHORT FINAL. 10-20 SECONDS LATER; APPROX 3 MI FINAL; TCASII RA ISSUED. TCASII DISPLAYED THIRD ACFT DIRECTLY IN FRONT OF US +2. LOOKED OUTSIDE AND SAW PIPER ARCHER DIRECTLY IN FRONT OF US AT OUR ALT IN LINE WITH US AND RWY 32R. RPTED TFC TO TWR AND DECLARED MISSED APCH. SHE RESPONDED THAT WE MUST BE LOOKING AT THE WRONG ACFT. WITH LITTLE TIME TO DEBATE BEFORE IMPACT; WE INITIATED A CLBING R TURN GAR. TWR INSTRUCTED TURN TO 360 DEGS AND 2500 FT. ON CLBOUT; GOT SECOND RA PRESUMABLY TRIGGERED FROM NUMEROUS ACFT ON R DOWNWIND FOR RWY 32R THAT WE WERE NOW FLYING TOWARD. CONCURRENT WITH THE SECOND RA AND A CONTINUATION OF THE R TURN TO AVOID THAT TFC; THE TWR ISSUED HDG OF 040 DEGS AND THEN 090 DEGS. AFTER ESTABLISHED ON 090 DEG HDG; RECEIVED THE THIRD RA FOR ACFT -2 AT 11 O'CLOCK POS. SUBSEQUENTLY RE-VECTORED BY APCH FOR VISUAL LNDG WITHOUT FURTHER INCIDENT. IT IS MY OPINION THAT THE ACFT POSING THE INITIAL COLLISION HAZARD WAS POSSIBLY SUPPOSED TO BE LNDG ON RWY 32L AND XGRESSED OUR APCH. IT IS ALSO MY OPINION; BASED UPON THIS EXPERIENCE AND NUMEROUS OTHER VISITS TO CMI; THAT SHARING THE PATTERN WITH UPWARDS OF 10 TRAINING ACFT PRESENTS A CHALLENGE TO A SAFE OP.