A B757-200 FLT CREW EXPERIENCED HIGH EGT SHORTLY AFTER TAKEOFF; FOLLOWED BY ENG VIB INDICATIONS. THEY COORDINATED WITH DISPATCH AND MAINT AND RETURNED TO DEP ARPT.

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JUST AFTER GEAR RETRACTION; ENCOUNTERED OVERHEAT CONDITION L ENG. RETARDED L THROTTLE TO BRING L ENG EGT WITHIN ACCEPTABLE OPERATING RANGE. CONTINUED CLB OUT OF ZZZ1 TERMINAL AIRSPACE AWAY FROM TFC. RADIOED DISPATCH OF ACFT STATUS. DISPATCH FACILITATED A 3-WAY COM WITH MAINT. AFTER A REAL TIME L ENG STATUS CHK; WE WERE INFORMED ON A MUCH LARGER SCALE THE ACFT HISTORY COVERING THE PREVIOUS 90 DAYS. APPARENTLY; ON ALL THE PAST 3 OR 4 MAX PWR TKOFS; THE ACFT HAD EXPERIENCED AN OVERHEAT CONDITION WITH THE L ENG. ADDITIONALLY; AT THIS TIME AS WE LEVELED OFF AT CRUISE ALT; WE NOTED A L ENG FAN VIBRATION ON LOWER EICAS PANEL OF 2.1. 2.4 MIGHT HAVE BEEN THE GREATEST VALUE. HOWEVER; WE ALSO NOTED A HULL VIBRATION THROUGH THE COCKPIT FLOOR ASSOCIATED WITH THE VIBRATION INDICATIONS. MAINT RESPONDED THAT OUR L ENG NEVER ENTERED INTO AN EGT RANGE OF 924 DEGS C FOR ANY LENGTH OF TIME; UP TO 20 SECONDS WAS PERMISSIBLE. MAINT FELT WE WERE AIRWORTHY; GOOD TO PRESS ON TO ZZZ. I ADDRESSED MY CONCERN WITH THE ACFT HISTORY; NOT BEING ABLE TO ACHIEVE MAX PWR FOR TKOF; WHICH IS A NORMAL OP FOR DEP OUT OF ZZZZ; SUCH AS CONTINGENCY FOR LOSS OF R ENG ON DEP ZZZZ; ETC. AFTER A BRIEF DISCUSSION WITH SOMEONE ELSE IN THE BACKGND AT DISPATCH; OUR DISPATCHER AGREED OUR EQUIP WAS NOT SUITABLE FOR OPS INTO ZZZZ. ENLIGHTENED OF THE FACTS; WE ALL AGREED THE ACFT NEEDED TO BE RETURNED TO ZZZ. THE L ENG VIBRATION SEEMED TO BE NEW INFO. IN ZZZZ'S AIRSPACE; WE NOTIFIED CTR OF OUR STATUS AND INTENTIONS TO RETURN TO ZZZ1. I EXERCISED CAPT'S AUTH; DECLARED AN EMER WITH ZZZ1 ATC. ALONG OUR RETURN FLT; WE DEVIATED W OF COURSE TO REMAIN WELL CLR OF WX; ACCOMPLISHED ASSOCIATED CHKLIST REGARDING OUR OVERWT LNDG AND NORMAL OPERATING PROCS. ZZZ1 ATC AND ZZZ1 CFR WERE ACCOMMODATING AND PROVIDED EXCELLENT COVERAGE OF OUR OP AT ALL LEVELS. MY CONCERN IS THE LACK OF SUPPORT REGARDING THE SAFETY OF OUR FLTS DIRECTLY FROM THE ACR EQUIP SUPVR. THERE DOESN'T APPEAR TO BE ANY ACFT RESEARCH/HISTORY REVIEW OR CONCERN FOR ACFT ABOUT TO BE TAKEN TO HIGH ALT PLACES LIKE ZZZZ1; ZZZZ2 OR REAL IMC INST OPS INTO ZZZZ3. EVERY CAPT ONLY HAS 1 HR TO DO THIS RESEARCH. PLTS ARE ONLY REQUIRED TO GO BACK IN THE LOGBOOK A FEW DAYS.