Regiments rhymes with:
argument's, arguments, armaments, complements, condiments, documents, elements, experiment's, experiments, filaments, impediments, implements, increments, instrument's, instruments, instruments', ligaments, monuments, ornaments, parliament's, parliaments, predicaments, sacraments, sediments, sentiments, supplements, temperaments, tenements, testaments, tournament's, tournaments
Regiments sounds like:
razzmatazz, reaganites, reagents, reassignments, recommends, recounts, regents, rescinds, resendes, resendez, resendiz, resents, resonates, rezendes, richmond's