INBOUND VFR PA31 AND DEPARTING GLF4 HAVE NMAC OVERHEAD PDX.

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I WAS INSTRUCTED BY PDX CTL TWR TO 'CROSS MIDFIELD AT 2000 FT FOR L DOWNWIND RWY 28L.' RWY 28L&R ARE STAGGERED BY AT LEAST 3000 FT (RWY 28L EXTENDS FURTHER W THAN RWY 28R). AS I CROSSED FROM N TO S AS INSTRUCTED; MIDFIELD FOR L DOWNWIND RWY 28L; A DEPARTING G4 ON RWY 28R CROSSED UNDERNEATH ME. I NEVER SAW THE G4 UNTIL HE WAS DIRECTLY UNDERNEATH MY ACFT. THE CTL TWR WAS USING ONLY 1 OF THEIR 2 FREQS DURING PEAK ARR AND DEP TIMES THUS LEAVING THE TWR EXTREMELY BUSY. AFTER THE G4 PASSED BELOW ME; HE RPTED THE NEAR MISS TO TWR. I BELIEVE THERE WERE SEVERAL CONTRIBUTING FACTORS: 1) THE STAGGERED RWYS OF 28L&R CAN CREATE MANY 'MIDFIELD' XING AREAS. WHAT IS CONSIDERED MIDFIELD AT PDX? 2) THE RATE OF CLB OF THE G4 AND MY AIRSPD WERE MISCALCULATED BY TWR. 3) THE TWR NEVER ANNOUNCED TA'S TO MYSELF OR THE G4; NOT EVEN AFTER IT WAS TOO LATE. MY OBSERVATION WAS THAT I CROSSED 'MIDFIELD' AND COMPLIED WITH TWR'S INSTRUCTIONS AS STATED. AFTER THE INCIDENT; ON THE GND TALKING WITH THE CTL TWR SUPVR; HE TOLD MYSELF AND MY ASSISTANT CHIEF PLT THAT THEY (TWR) NEVER SAW THE CONFLICT BECAUSE THEY (TWR) WERE LOOKING THE OPPOSITE DIRECTION.