B737-200 CREW HAD LESS THAN LEGAL SEPARATION WITH A VFR ACFT AND AN A-319 IN N90 CLASS E.

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ON CLBOUT FROM EWR; ATC GAVE US A CLB CLRNC TO 12000 FT AT 250 KTS. PASSING COLTS NECK VOR; ATC GAVE US A L TURN TO 120 DEGS FOR IN TRAIL SPACING WITH TFC OVER WHITE INTXN. PASSING AROUND 7700 FT ON A 120 DEG HDG; I NOTICED THE TFC DISPLAY ON TCASII AT 12 O'CLOCK POS AND 1200 FT ABOVE AT ABOUT 3-4 MI. AS IT WAS OBVIOUS TO ME THAT A CONTINUED CLB INTO THIS TFC WOULD CAUSE CONFLICT; I TOLD THE FO; WHO WAS HAND FLYING; TO SHALLOW OUT HIS CLB. ATC THEN CALLED OUT THE TFC AS VFR; 12 O'CLOCK POS 8900 FT. I TOLD ATC (NEW YORK DEP) THAT WE SAW HIM ON TCASII AND WERE STOPPING CLB TO AVOID A CONFLICT. HE SAID 'THAT'S APPROVED' OR 'OK.' THE FO STOPPED THE CLB AT 8200 FT. TCASII CALLED OUT 'TFC; TFC.' AS WE CONTINUED TO MONITOR THE VFR TFC; ANOTHER TARGET APPEARED AT ABOUT 1-2 MI BEHIND HIM; ALSO AT 12 O'CLOCK POS AND 200 FT BELOW OUR ALT. IT APPEARED ON THE VSI TCASII DISPLAY ALREADY IN YELLOW (CAUTION) WE WERE QUICKLY BEING SANDWICHED BTWN THOSE 2 ACFT. I IMMEDIATELY TOLD MY FO TO TURN HARD R; AS I COULD TELL THAT ALT WAS OF NO USE. ALMOST AS SOON AS I SAID THIS; ATC TOLD US TO TURN R TO 240 DEGS AND CLB TO 12000 FT. THE SECOND TARGET (AN A319) WAS NOW SO CLOSE THAT THE TCASII COMMANDED 'DSND; DSND NOW' (TO 1500 FPM DOWN). THIS WAS CONTRARY TO ATC; BUT WE IMMEDIATELY FOLLOWED IT; AS I CALLED ATC AND SAID 'NEGATIVE; WE HAVE AN RA TO DSCNT. WE ARE GOING DOWN.' HE RESPONDED 'ROGER.' AS WE WERE BANKING HARD R; I SAW THE VFR TFC PASS OVER US AND THE A319 BANKING HARD L AND CLBING (?) TO AVOID US. CLOSEST ESTIMATED DISTANCE WAS 1 1/2-2 MI AND 200-300 FT. AFTER WE CLRED THE CONFLICT AND CONTINUED OUR CLB; I ASKED ATC WHAT WENT WRONG. HE VAGUELY STATED HE THOUGHT WE WOULD BE ABLE TO CLB ABOVE THE VFR TFC BEFORE IT WOULD BECOME A CONFLICT. THIS WAS DEFINITELY A VERY UNLUCKY SET OF CIRCUMSTANCES THAT LED TO A CLOSE CALL WITH 2 ACFT. IT HIGHLIGHTS AGAIN THAT YOU SHOULD FOLLOW THE RA AND NOT ATC'S INSTRUCTIONS.