There is no English word that meets the criteria. However, here
are some words you can make if you repeat some of the letters.
deemster, dempster, demurest, demurred, demurrer, depermed,
deserted, deserter, desserts, deterred, deterrer, detested,
detester, detruded, detrudes, dressers, drummers, duresses,
eremurus, esteemed, estruses, meseemed, murdered, murderee,
murderer, murmured, murmurer, musettes, mustered, muttered,
mutterer, peppered, pepperer, perdured, perdures, permuted,
permutes, perusers, pestered, pesterer, preempts, pressers,
pressure, presters, presumed, presumer, presumes, pretests,
purpures, pursuers, puttered, putterer, redeemed, redeemer,
repumped, repursue, reseeded, resetter, restress, resumers,
retemper, retested, reutters, rumpuses, ruptured, ruptures,
semester, septette, smeddums, speeders, speedups, spudders,
spurrers, sputters, steepers, steepest, steerers, stemmers,
steppers, stressed, stresses, strummed, strummer, strumpet,
strutted, strutter, stumpers, stutters, summered, sumpters,
suppress, supremer, susurrus, teetered, tempered, temperer,
tempests, tempters, tressure, trumpets, trussers, trusteed,
trustees, trusters, turreted, upsetter, usurpers, uteruses,
utterers