WW24 FLC EXECUTES EVASIVE TCASII CLB AND CLBS ABOVE ASSIGNED DEP ALT. ATC FLC REVIEW WITH TWR CTLR AND SUPVR AND TRACON SUPVR DOES NOT SATISFY PIC'S CONCERNS WITH NMAC INCIDENT.

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IFR CLRNC RECEIVED. CLRED TO TAKE OFF AND CLB TO 3000 FT. WERE GIVEN VECTOR AND ASSIGNED HDG. AT 2900 FT; CAPT (PNF) SAW CONFLICTING TFC AT APPROX SAME ALT. EVASIVE ACTION TAKEN. OUR ACFT CLBED TO AVOID MIDAIR. CLB RESULTED IN AN ALTDEV OF 500 FT (TO 3500 FT). TFC SHOULD HAVE BEEN CTLED TO AVOID THIS. SUPPLEMENTAL INFO FROM ACN 397125: PWK TWR CLRED WESTWIND JET FOR TKOF ON RWY 34; L TURN HDG 290 DEGS; CLB AND MAINTAIN 3000 FT. I NOTICED AN ACFT IN THE PLT'S WINDSHIELD. AT THAT POINT; I TOOK CTL OF THE AIRPLANE AND BEGAN CLBING AS TCASII SOUNDED. I WAS ABLE TO AVOID A MIDAIR COLLISION BY CLBING ABOVE THE OTHER ACFT. THE PF DID NOT SEE THE OTHER ACFT BECAUSE IT ALL HAPPENED SO QUICKLY. IT IS MY BELIEF THAT WHILE ON AN IFR FLT PLAN; WE SHOULD HAVE HAD AN EXTRA MARGIN OF SAFETY. AFTER MISSING THE OTHER ACFT I ADVISED THE TWR CTLR AND TRACON OF THE NMAC AND REQUESTED THAT THEY HOLD THE TAPES. ONCE I LANDED AT MKE; I TELEPHONED TWR AND TRACON. THE TWR CTLR AND HIS SUPVR WERE BOTH VERY ADAMANT IN THEIR BELIEF THAT WE WERE OUTSIDE OF THEIR ATA AND ADVISED THAT THE SIT WAS BEYOND THEIR CTL.