A B727-200 ENCOUNTERED FORECAST WINDSHEAR ON 2 APCHS TO SLC AND EXECUTED MISSED APCHS WITH TCASII WARNING. DURING THE SECOND WINDSHEAR AVOIDANCE MANEUVER; THE ACFT EXPERIENCED SEVERE WINDSHEAR WHICH REQUIRED ENOUGH THRUST TO OVERBOOST ENGS #2 AND #3.

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ON APCH TO SLC; NOTIFIED THAT AN ACFT HAD GONE AROUND FOR WINDSHEAR; BUT OTHERS HAD LANDED. INITIATED APCH AND NOTED THAT WINDS HAD GONE FROM 180 DEGS 25 KTS GUSTING TO 35 KTS; TO 360 DEGS 25 KTS GUSTING TO 35 KTS. GOT A 20 KT INCREASE AT ABOUT 1200 FT AGL AND WENT AROUND. ALSO GOT TCASII WINDSHEAR WARNING. WENT TO FAIRFIELD TO HOLD AND WAS TOLD OTHER ACFT HAD LANDED. INITIATED ANOTHER APCH AND AGAIN GOT INCREASE OF +20 KTS AT APPROX 1000 FT AGL. ALSO GOT WINDSHEAR WARNING. THEN ON THAT GAR AT APPROX 2500 FT AGL; GOT ANOTHER TCASII WARNING AND ACFT SHUDDERED AND LOST AIRSPD AND SOME ALT (NOT SURE HOW MUCH). FULL FIREWALL PWR APPLIED. DIVERTED TO LAS. WHEN WINDS CHANGE DIRECTION AND ARE AT STRAY; THIS CREATES UNSTABLE AREA. BETTER MEASURING INSTS MIGHT HAVE PICKED UP THE WINDSHEAR. SUPPLEMENTAL INFO FROM ACN 426752: WHILE CLEANING UP AND ACCELERATING THROUGH 6500 FT MSL; GOT A HUGH AIRSPD LOSS AND WINDSHEAR ANNUNCIATION. THIS TIME WITH FIREWALL THRUST. ENRTE; CONTACTED DISPATCHER AND MAINT. ARE RELUCTANT TO TRY AGAIN AT SLC DUE TO POSSIBLE OVERBOOST OF ENGS. DUE TO TANKERED FUEL; ARE FAT ON GAS. JOINTLY AGREE TO DIVERT TO LAS DUE TO FORECAST WX AND MAINT CAPABILITY. ADVISED ENGS #2 AND #3 WERE OVERBOOSTED REQUIRING AN ENG CHANGE. ALSO ADVISED TO SUBMIT NASA FORM FOR CYA.