AN ACR MLG ON APCH INTO HPN RECEIVES NUMEROUS TCASII ALERTS IN VICINITY OF THE ARPT. WHILE ESTABLISHED ON FINAL; THEY REACT TO AN RA AND COME CLOSE TO A VFR SMALL ACFT PASSING BELOW THEM.

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BTWN ABEAM DOWNWIND AT HPN AND THE OM (CLUBY) FOR RWY 34 AT HPN HAD 5 RA'S FOR LIGHT ACFT. WE WERE AT 3000 FT ASSIGNED AND BEING VECTORED BY NY APCH; AUTOPLT ON. THE LIGHT ACFT WERE AT 2500 FT AND 3500 FT; SO OUR FIRST 4 RA'S WERE 'MONITOR VERT SPD' WITH NO EVASIVE ACTION REQUIRED; WE SAW THEM AND TCASII SHOWED 400-600 FT SEPARATION. ON FINAL; ABOUT 1 MI OUTSIDE OM; SUN JUST SETTING AT OUR 11 O'CLOCK POS (IN OUR EYES) WE'RE TRYING TO GET VISUAL CONTACT WITH TFC AT 10 O'CLOCK POS; 1 MI; 500 FT BELOW US. WE'RE STILL AT 3000 FT ASSIGNED (GS AT THE MARKER IS 1804 FT); WE'VE SLOWED TO 170 KTS; FLAPS 10 DEGS. WE GET RA OF 'CLB; CLB.' I DISENGAGE AUTOPLT AND CLB; TCASII SHOWED 300 FT SEPARATION; FO SAW ACFT PASS DIRECTLY BELOW US AT ABOUT 200 FT; WE CLBED TO ABOUT 3200 FT; THEN APCH CLRED US FOR THE APCH (AFTER WE CALLED VISUAL CONTACT AND CLR OF ACFT). WE ARE NOW OVER OR JUST INSIDE THE MARKER; EXTEND GEAR AND FLAPS; TWR CALLED AND CLRED TO LAND; LANDED SAFELY. WHEW. I CALLED TWR AND NY TRACON; FILED NEAR MISS RPT WITH NY TRACON; THEY SAID THE OTHER ACFT WAS NOT UNDER THEIR CTL. I HAVE HEARD 'HORROR STORIES' FROM OTHER PLTS ABOUT HPN; SO THIS LOOKS LIKE A SYS PROB. LET'S CHANGE THINGS AND GET IT MOVING IN A POSITIVE DIRECTION BEFORE WE HAVE A BODY COUNT. SUPPLEMENTAL INFO FROM ACN 409144: THIS OCCURS MORE OFTEN THAN NOT AT HPN. IT IS UNACCEPTABLE SEPARATION FOR AIRLINES TO OPERATE SAFELY UNDER THESE CONDITIONS. 500 FT VERT SEPARATION IS NOT ADEQUATE SEPARATION BTWN AN AIRLINER AND VFR GA ACFT. ATC TOLD US THAT THIS WAS ALL THEY WERE RESPONSIBLE FOR. HOWEVER; YOU HAVE NO IDEA WHAT THE QUALIFICATIONS OF THE PLT IN THE SMALL ACFT ARE. THEY COULD BE A STUDENT PLT OUT ON A SOLO FLT. CAN WE HONESTLY EXPECT THAT THEY WILL ALWAYS HOLD ALT PERFECTLY. OBVIOUSLY NOT; IN THIS CASE; WHERE THEY CLBED 300 FT RIGHT UNDERNEATH US. ATC SHOULD NOT HAVE VECTORED US NEAR THAT ACFT. WE NEED TO DO SOMETHING WITH THE SYS AT THESE ARPTS WHERE THERE IS A HIGH VOLUME OF GA AND TRAINING TO PROVIDE MORE ADEQUATE SEPARATION BEFORE THERE IS A SERIOUS ACCIDENT.