DC8-73 FLT CREW MAKES THREE REJECTED TKOFS ACCOUNT TKOF WARNING HORN SOUNDING.

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AFTER CONDUCTING AN UNEVENTFUL PREFLT; THE CAPT LINED UP TO PERFORM A REDUCED THRUST TKOF. EXCEEDING 40% ON ALL ENGS THE PLT RELEASED BRAKES AND ADVANCED THE THROTTLES TO APPROX TKOF THRUST. AS ENGS ACCELERATED PAST 80%; THE TKOF WARNING HORN SOUNDED CAUSING THE CAPT TO REJECT THE TKOF AROUND 30 KTS. I NOTIFIED TWR AND REQUESTED TO CLR THE RWY SO WE COULD EVALUATE THE SITUATION. AFTER ENSURING THE FLAP HANDLE/GAUGE WERE AT TKOF SETTING (18 DEGS) AND THE SPOILER LEVER FULL FORWARD (SPOILER EXTEND LIGHT NOT ILLUMINATED); THE CREW RESEARCHED THE AOM AND SYS MANUAL TO ENSURE NO OTHER SYS TRIGGERED THE HORN. I DREW UPON MY MIL MAINT EXPERIENCE AND SUGGESTED WE RECYCLE BOTH SYS AND TRY IT AGAIN. RECYCLING BOTH SYS AND PERFORMING AND ENG RUN TO 70% (ADVANCING THROTTLES BEYOND IDLE STOP; APPROX 1.5 INCH OF THROTTLE MOVEMENT; TRIGGERS THE HORN) THE CAPT CALLED MAINT CTL AND ADVISED THEM OF OUR ACTIONS AND OUR INTENT TO PERFORM ANOTHER TKOF. MAINT CTL STATED THAT THEY COULD NOT THINK OF ANY FURTHER ACTIONS AND CONCURRED WITH A SECOND TKOF ATTEMPT. FOLLOWING A BRIEF TAXI; THE CAPT ONCE AGAIN PERFORMED A REDUCED TKOF ATTEMPT. THE CAPT ADVANCED ALL 4 ENGS TO 70% (GREATLY EXCEEDING 1.5 INCH THROTTLE MOVEMENT) THEN RELEASED BRAKES. AFTER SETTING THE TKOF THRUST THE TKOF WARNING HORN SOUNDED WHEN N1 EXCEEDING 80%. THE CAPT ONCE AGAIN PERFORMED A LOW SPD REJECTED TKOF. THE CAPT DIRECTED THE CREW TO NOTIFY ALL APPLICABLE AGENCIES FOR A BLOCK TURN-BACK. UPON ARRIVING IN THE SPOT; MAINT PERFORMED APPLICABLE CHKS/UPLOADED FUEL (ROUGHLY 1 HR) AND COULD NOT DUPLICATE THE CONDITION. AFTER SIGNING OFF THE WRITE-UP; THE CAPT PREPARED THE ACFT FOR ANOTHER REDUCED THRUST TKOF. AFTER NUMEROUS END-OF-RWY CHKS; THE TKOF WARNING HORN DID SOUND AS THE ENGS EXCEEDED 80%. ONCE AGAIN THE CAPT PERFORMED A LOW SPD REJECTED TKOF AND COORDINATED YET ANOTHER BLOCK TURN-BACK. KNOWING THAT THE TKOF WARNING HORN SHOULD BE ARMED BY THROTTLE POS; NOT ENG SPD; THE CREW RETURNED THE JET TO MAINT. LOOKING BACK AT THE EARLY MORNING EVENTS; THE CREW SHOULD NOT HAVE CONDUCTED THE SECOND TKOF ATTEMPT. ONCE THE CREW REJECTED TKOF FOR A NON-DEFERRABLE SYS; AND DID NOT DETECT ANY OBVIOUS DEFICIENCIES THAT COULD ACTIVATE THE HORN; I SHOULD HAVE NOT SUGGESTED RECYCLING THE SYS AND ATTEMPTING ANOTHER TKOF. LACKING COMPLETE SYS KNOWLEDGE AND UNABLE TO VISUALLY VERIFY THE FLAPS AND SPOILERS; MY PAST EXPERIENCE NEGATIVELY INFLUENCED ME. THE SYS SHOULD HAVE BEEN WRITTEN UP AND PRESENTED TO MAINT SO THAT ALL APPLICABLE INSPECTIONS COULD BE CONDUCTED. MAINT CTL COULD HAVE EASILY ENCOURAGED THE CREW TO WRITE UP THE TKOF WARNING SYS (NON-DEFERRABLE) AND PERFORM A BLOCK TURN-BACK. IT TAKES A TEAM EFFORT TO BREAK THE ERROR CHAIN.