SMT AND SMA HAVE NMAC UNDER FLOOR OF TCA.

Narrative

WE CLBED TO 2700' MLS NAVIGATING TO BWZ VOR. FLOOR OF NY TCA IS 3000' IN THIS AREA. WE HAD CONTACTED NY APCH ON 119.2 TO REQUEST A TCA CLRNC TO CLB VFR TO 6500' DIRECT TO BWZ VOR. THEY ASKED US TO CONTACT NY ON 127.6. AFTER TUNING TO NEW FREQ; PNF OBSERVED TFC AT 12 O'CLOCK AND CLOSING; SAME ALT OR SLIGHTLY ABOVE (OPP DIRECTION). PNF THEN TOOK CTLS AND MADE AN IMMEDIATE 45 DEG BANK AND DIVE TO RIGHT TO AVOID ENCOUNTER. WE ESTIMATED IN PASSING THE SMA WAS APPROX 150 YDS TO OUR 9 O'CLOCK POS AND ABOUT 100' ABOVE OUR ALT. THE SMA TOOK NO EVASIVE ACTION AND APPARENTLY DID NOT SEE US. WE WERE NOT IN RADIO CONTACT WITH APCH AT THE TIME. WE COULD HAVE BEEN MORE VIGILANT. TOO MANY ACFT IN NY AREA TRYING TO SKIRT UNDERNEATH FLOOR OF TCA IS MAJOR FACTOR CONTRIBUTING TO THIS INCIDENT. EVEN WHEN TALKING TO APCH WITH TFC ADVISORIES; NOT ALL TFC IS CALLED DUE TO CTLR WORKLOADS AND AIRSPACE SATURATION. SUGGESTION RADIO CONTACT TO A CTLING FAC FOR ALL ACFT IN AREA. THIS; OR COURSE; MEANS ADDITIONAL CTLRS TO HANDLE THE WORKLOAD.