LGT AND SMT HAVE NEAR MIDAIR COLLISION.

Narrative

WE WERE DSNDED DOWN TO 4000' MSL. DSCNT CHKLIST WERE COMPLETE; ALTIMETERS SET TO BDL SETTINGS. CAPT'S AND COPLT'S ALTIMETERS WERE WITHIN +/-25'. WHILE LEVEL AT 4000' APPROX 3 MI S OF ARPT; APCH CALLED TFC 11:30-12 O'CLOCK POS; 3500' AND 2 MI. WE RESPONDED; 'NO JOY.' 30 SECS LATER WE; COPLT AND MYSELF; SPOTTED TFC 12 O'CLOCK AT OUR ALT LESS THAN 1000' PASSING W TO E. WE HARDBANKED LEFT; HE DID THE SAME; PASSING OFF RIGHT WING TIP. APCH ASKED THE ACFT; A TWIN ENG SMT; WHAT HIS ALT WAS. NO ANSWER. HE ASKED AGAIN; NO ANSWER. WE WERE SWITCHED OVER TO TWR CTL AND HEARD NOTHING MORE. FLT CREWS FIRST LEG TOGETHER WITH NO PROBS. THE WX WAS A LOW LYING HAZE; TOPS ABOUT 2000'. WHY THEN DIDN'T WE SEE THE TFC? THREE SETS OF EYES WERE LOOKING FOR HIM. BETTER YET; WHY DIDN'T HE SEE US? ALL LIGHTS WERE ON ON A FAIRLY LARGE ACFT (LGT)? CORRECTIVE ACTION TO THE LEFT BECAUSE OF HIS DIRECTION OF FLT. IF WE TURNED RIGHT IT WOULD HAVE BEEN DISASTROUS. IT SEEMS A TCA WOULD HAVE DEFINITELY HELPED. I THINK ATC IS CUTTING ACFT TOO CLOSE TO ACCOMMODATE TOO MANY ACFT AT ONE TIME--ESPECIALLY GA AND TRANSPORT. THEY MUST REMEMBER WHO PAYS TO USE THE ARPTS AND GIVE PRIORITY TO THE TRANSPORTS. LET'S RECOMMEND TO KEEP THE F/E'S POS FOR IF EVEN THE SIMPLE FACT OF 3 SETS OF EYES ARE BETTER THAN 2. IN THIS CASE; IT PROBABLY WOULD HAVE ENDED IN TRAGEDY W/O ONE.