JUST AFTER TKOF WDB EXPERIENCES ENG FIRE WARNING AND PERFORMS AN INFLT ENG SHUTDOWN. FUEL DUMPED AND ACFT PROCEEDS IN A DIVERSION TO ALTERNATE ARPT FOR 'AVAILABLE SUPPORT.'

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SHORTLY AFTER TKOF #4 ENG EGT BEGAN INCREASING. SO RETARDED #4 THRUST LEVER TO KEEP TEMP WITHIN LIMITS; AIRBORNE VIBRATION MONITOR SHOWED INCREASE. LEVELED AT 6000 FT MSL TO STAY BELOW CLOUDS AND ADVISED ATC OF POTENTIAL PROBLEM. CONTINUED RETARDING #4 THRUST LEVER AS EGT AND FUEL FLOW SHOWED RISING TREND. EXPERIENCED ONE COMPRESSOR STALL FOLLOWED BY #4 ENG FIRE WARNING. SHUT DOWN ENG; DISCHARGED BOTTLE. WARNING LIGHT OUT AFTER 25 SECONDS. ADVISED ATC AND REQUESTED RADAR VECTORS TO REMAIN IN DEP CTL AREA AND ADVISED FUEL DUMPING WOULD BE NECESSARY. CONTACTED MSP DISPATCH TO COORD COURSE OF ACTION. DECISION MADE TO FLY TO MSP. REQUESTED AND RECEIVED ATC CLRNC -- FUEL DUMPING APPROVED DURING CLB NW OF STL. DUMPED TO WT TO ALLOW CRUISE AT 220. MSP DISPATCH PROVIDED FLT PLAN INFO INCLUDING ENRTE TIME; FUEL FIGURES AND WX. UPON CONTACT WITH MSP CTR AND ASCERTAINING WX AND TFC; DUMPED ADDITIONAL FUEL TO ASSURE LNDG WT OF 585000 POUNDS. LANDED WITHOUT INCIDENT AT MSP. CHOICE OF ARPTS INFLUENCED BY FAMILIARITY AND AVAILABLE SUPPORT.