After the TEA-EAT-ATE anagram box:
I thought the related POT (teapot) might work as well, with OPT and TOP other words from those letters, but doesn’t work three-ways; only working two-ways from any combination:
Starting with TOP and OPT leaves PTO at the end; it is an acronym for Please Turn Over, but not a word:
Starting with OPT and POT leaves TTO:
Starting with POT and OPT also leaves TTO
I guess a word with two vowels might be needed. Do you know any others that work?