FLC CLBS INTO AN NMAC WITH KNOWN VFR TFC.

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THE FO WAS FLYING THE LEG. WE WERE CLRED TO 17000. WE CONTACTED BOSTON CTR AND HE ADVISED US TO LEVEL AT 10000 AND CALLED VFR TFC HDG EBOUND AT 1:30 POS 11500 FT. WE CALLED THAT TFC IN SIGHT AND WERE CLRED TO 'REF THAT TFC CLB TO 17000.' I WATCHED THE TFC AND NOTIFIED THE CAPT THAT IT WAS 'CONSTANT BEARING; DECREASING RANGE.' HE ACKNOWLEDGED THAT AND TOLD THE FO TO INCREASE THE RATE OF CLB. THE FO INCREASED THE RATE OF CLB. ABOUT 10 SECONDS LATER THE TFC APPEARED MUCH CLOSER THAN IT DID WHEN WE HAD FIRST SIGHTED IT. WE WERE AT 10900 FT AND THE CAPT INSTRUCTED THE FO TO PUSH IT OVER. THE FO PERFORMED A MILD PUSH OVER. CLB RATE DECREASED FROM APPROX 2000-1000 FPM. THE ACFT CONTINUED TO CLB AND THE CAPT SHOUTED 'LEVEL OFF' AND PUSHED FORWARD ON THE CTL COLUMN. WE LEVELED AT 11250 JUST AS THE COMMUTER PLANE PASSED DIRECTLY OVERHEAD. WHAT CAUSED THE PROBLEM. WE SAW THE ACFT AND ASSUMED THAT IT WAS SUFFICIENTLY FAR AWAY DUE TO ITS RELATIVE SIZE IN THE WINDSCREEN. IT WAS ACTUALLY MUCH CLOSER THAN WE THOUGHT BECAUSE IT WAS A TWIN ENG COMMUTER PLANE. THE CAPT DID NOT TAKE ADEQUATE ACTION TO COM TO THE FO HIS DESIRE FOR HIM TO LEVEL THE ACFT AT 11000 FT. THIS WAS WAY TOO CLOSE. IT DEFINITELY WOULD HAVE BEEN A MID AIR COLLISION. WE MUST HAVE LOOKED HUGE TO THAT COMMUTER.