ERJ 170 CLIMBED IN RESPONSE TO A TCAS 'RA' WHICH RESULTED IN A 'DESCEND' RA FOR IFR TFC 1000 FT ABOVE.

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AFTER EXECUTING A VERY CLOSE GAR MANEUVER; WE WERE HANDED OFF TO APCH CTL FOR VECTORS BACK TO LAND. AFTER MAKING AN ANNOUNCEMENT TO THE PAX; WE CONTINUED TO TURN DOWNWIND UNDER THE GUIDANCE OF APCH CTL. AT APPROX MID-FIELD; I NOTICED THAT THERE WAS TFC 300 FT BELOW US ON AN INTERCEPTING COURSE AND TOLD MY FO TO BE PREPARED. HE THEN BROUGHT IT TO APCH CTL'S ATTN. THEY REPLIED THAT THE TFC WAS VFR AND NO FACTOR. HE TOLD THEM HOW CLOSE IT WAS AND AT THAT MOMENT WE RECEIVED AN RA WITH INSTRUCTIONS TO CLB AND AN ACCENT BOX TO STEER INTO. HE INFORMED THEM OF OUR INTENTIONS AS I POWERED UP AND PITCHED INTO THE 'BOX' TO AVOID THIS CONFLICT. APCH RESPONDED THAT WE WERE NOT TO CLB; THAT WE HAD ENOUGH SEPARATION AND THAT THERE WAS A DASH 8 1000 FT ABOVE AND IN FRONT OF US. MY FO ARGUED FOR OUR SITUATION AND HAVING A VISUAL ON THE DASH 8 TOLD HIM TO ADVISE THAT I AM BANKING L BEHIND THE DASH 8 AND CLBING TO AVOID THE OTHER PLANE. I CLEARED THE FIRST PLANE BY 800 FT AND RECEIVED ANOTHER RA IN RESPONSE TO THE DASH 8. I BROUGHT THE PWR TO NEAR IDLE AND PUSHED THE NOSE OVER FOLLOWING THE COMMANDS (BOX). I RETURNED TO THE ASSIGNED ALT OF 3000 FT AND RESUMED OUR APCH FOR A LNDG. AFTER DEPLANING; I CONTACTED OUR CHIEF PLT AND THE TWR WHICH TRIED TO MAKE LIGHT OF WHAT TRANSPIRED AND OFFERING A VERY WEAK CASE ON THEIR BEHALF. PLEASE DO NOT LET EITHER OF THESE INCIDENTS GO WITHOUT STAFF BEING ACCOUNTABLE AND THE FAA TO INSPECT THIS. IT IS INCOMPREHENSIBLE HOW ONE FLT CREW COULD BE SUBJECTED TO SUCH A LACK OF PROFESSIONALISM. SUPPLEMENTAL INFO FROM ACN 783437: AFTER HAVING THE RWY INCURSION AND GOING MISSED AND THEN HAVING AN RA ADVISORY AND ACTION TAKEN FOR THE INTEREST OF SAFETY AND ALSO ARGUING WITH APCH ON HAVING THEM DENY OUR RA SAFETY MANEUVER TO AVOID TFC; WE HAD ANOTHER RA TO AVOID AN ACFT ABOVE US. THIS WAS 3 INCIDENTS WITH TWR AND APCH WITHIN 5 MINS. 1 RWY INCURSION AND 2 RA MANEUVERS.