B737-300 ON ARR HAS NMAC WITH SECOND ACFT.

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B737-300; BUF-LGA; EXTOL 2 ARR. CLRED DIRECT TO VALRE INTXN; MAINTAINING 15000 FT MSL; APPROX 3000 FT MSL ABOVE A PROFILE DSCNT TO CROSS BAYSE INTXN AT 8000 FT MSL. ON TOP IN VMC NIGHT CONDITIONS. AUTOPLT IN USE. RECEIVED A DSCNT CLRNC TO MAINTAIN 10000 FT MSL AND THE CAPT COMPLIED. DSNDING THROUGH 14000 FT MSL THE CTLR ISSUED A CLRNC TO EXPEDITE THE DSCNT TO 10000 FT MSL AND THE CAPT COMPLIED. OUR INDICATED AIRSPD AT THIS TIME WAS BTWN 270- 280 KTS. THE CAPT WAS IN THE LEVEL CHANGE MODE AND UPON HEARING THE CLRNC TO EXPEDITE; HE SIMPLY SELECTED A HIGHER AIRSPD TO DSND AT APPROX 320 KTS. THIS ALLOWED THE ACFT TO DSND AT APPROX 5000 FPM. AT APPROX 12500 FT MSL THE CTLR REVISED THE CLRNC TO MAINTAIN 11000 FT MSL. SAID VFR TFC WAS 12:30 TO 1:00 O'CLOCK WBOUND AT 10500 FT. THE CAPT CHANGED THE ALT ON THE MCP TO 11000 FT AND ALT ACQUIRED ANNOUNCED ON THE AUTOPLT DISPLAY. THE AUTOPLT ATTEMPTED TO LEVEL THE ACFT; BUT THE RATE OF DSCNT WAS TOO GREAT. THE CAPT DISCONNECTED THE AUTOPLT AS THE ACFT WAS APCHING 11000 FT AND MANUALLY BROUGHT THE ACFT'S HIGH RATE OF DSCNT UNDER CTL; BUT NOT UNTIL LEVELING OFF AT 10300 FT MSL. WHEN THE CAPT MANUALLY TOOK CTL OF THE ACFT; I DIVERTED MY ATTN OUTSIDE THE ACFT IN AN ATTEMPT TO ACQUIRE THE VFR TFC VISUALLY. WHEN I SAW THE TFC SLIGHTLY ABOVE OUR ALT; I TOLD THE CAPT I HAD IT IN SIGHT AND TO CONTINUE A DSCNT SO WE WOULD NOT CLB BACK INTO THE OTHER ACFT. I PUT MY HANDS ON THE CTLS AS TO NOT ALLOW THE ACFT TO ASCEND. THE VFR TFC PASSED IN FRONT OF US; SLIGHTLY FROM R TO L; APPROX 200 FT ABOVE OUR ALT. AFTER THE TFC WAS CLR; I BROUGHT MY ATTN BACK INTO THE COCKPIT AND OBSERVED OUR ALT AT APPROX 10300 FT MSL. I RADIOED ATC TO INFORM HIM THAT WE MADE A DEV FROM OUR NEW ASSIGNED ALT TO AVOID TFC; AND THAT WE WERE BEGINNING TO CLB BACK TO OUR LAST ASSIGNED ALT. ATC ISSUED A NEW CLRNC TO MAINTAIN 9000 FT MSL AND SAID NOTHING OF THE ALTDEV. THE REST OF THE FLT PROCEEDED WITHOUT INCIDENT. TCASII ISSUED NO WARNINGS.