A PA60 FLYING THROUGH PBI; FL; AIRSPACE HAS AN NMAC WITH AN ACR MAKING AN APCH BENEATH HIM.

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WHILE CRUISING BELOW THE CLOUDS AT 2000 FT MSL FROM SUA TO BCT; I WAS RECEIVING RADAR ADVISORIES FROM PBI. AFTER PASSING DIRECTLY OVERHEAD THE ARPT; I PROCEEDED SEBOUND TOWARDS BCT. ABOUT 5 MI SW OF PBI; ENCOUNTERED MODERATE TURB AND UPDRAFTS AND DOWNDRAFTS. I REDUCED PWR BUT THE UPDRAFT WAS STRONG ENOUGH THAT THE AUTOPLT DISCONNECTED AND WITH THE PITCH DOWN TRIM THAT THE AUTOPLT HAD USED TO COUNTER THE UPDRAFT; THE NOSE PITCHED DOWN. I ASSUMED CTL IMMEDIATELY AND LOST NO MORE THAN 150 FT; CORRECTING BACK TO 2000 FT ALMOST IMMEDIATELY. A COMMERCIAL JET WAS MAKING AN APCH BELOW ME AT 1500 FT TO RWY 13/31 AT PBI. THE CTLR TOLD ME THAT HE HAD RECEIVED AN RA AND HAD TURNED AWAY AND CLBED. I REMAINED AT 2000 FT UNTIL I PASSED BEHIND THE JET AND THEN DSNDED INTO BCT. SUPPLEMENTAL INFO FROM ACN 394250: WHILE BEING VECTORED FOR THE VOR 31 AT PBI; ATC ISSUED VFR TFC AT 11-12 O'CLOCK; 500 FT ABOVE US. WE WERE ON THE VOR TO RWY 31 AT 1500 FT. THE VFR WAS LEVEL AT 2000 FT. THERE WAS MODERATE TURB IN THE AREA. ALL OF A SUDDEN THE TFC DSNDS TOWARDS US. WE RECEIVED TCASII TA FOLLOWED BY AN RA (TCASII) TO DSND AT APPROX 1000-1500 FPM. SINCE WE WERE AT 1500 FT; I BANKED TO THE L WITH A 45-50 DEG BANK; MONITORING TCASII AS WE TURNED AWAY. ONCE CLR OF CONFLICT WAS ANNUNCIATED; WE INFORMED ATC OF THE INCIDENT. THEY TOLD US THE TFC WAS TOLD TO MAINTAIN 2000 FT. I SUSPECT THE VFR TFC; AN AEROSTAR; COULD NOT MAINTAIN ALT DUE TO THE TURB. INSTEAD OF ATTEMPTING A FOURTH APCH (THIS WAS OUR THIRD); WE DIVERTED TO MIA FOR FUEL AND TO ALLOW THE WX TO MOVE THROUGH THE PBI AREA. CTLR STATED THE VFR PLT WAS 'SHAKEN' WHEN ATC SPOKE TO THEM ON THE GND.