Here's what rhymes with nonquaternary.
marry merry ternary nary very ordinary vary fairy bury dairy ferry wary cherry hairy berry sherry tarry canary parry unwary harry tare barre terry faerie wherry customary coronary dietary urinary prairie honorary papillary scary cautionary remarry buffoonery legionary pessary apiary nondairy uncustomary temporary arbitrary missionary monetary pulmonary capillary commentary dictionary hereditary imaginary solitary stationary adversary legendary pituitary visionary corollary dysentery mercenary sedentary seminary veterinary apothecary commissary emissary itinerary stationery centenary luminary aviary bacillary actuary equerry humeri lapidary bilberry elderberry topiary plagiary necessary military literary secondary monastery cemetery disciplinary momentary sanitary unitary ancillary budgetary estuary planetary culinary fiduciary funerary mortuary obituary sanguinary statuary dignitary beriberi breviary diversionary cassowary dromedary tercentenary chokecherry nonhereditary sectary contemporary extraordinary secretary preliminary unnecessary evolutionary sanctuary subsidiary involuntary judiciary maxillary pecuniary proprietary reactionary tributary inflationary salutary functionary savagery confectionery deflationary epistolary expeditionary probationary supernumerary tutelary unsanitary nonmilitary concessionary huckleberry recessionary voluptuary nonliterary revolutionary vocabulary beneficiary fragmentary discretionary interdisciplinary exclusionary expansionary genitourinary paramilitary constabulary insanitary geostationary bicentenary elocutionary interplanetary eleemosynary cardiopulmonary multidisciplinary undersecretary counterrevolutionary Words that almost rhyme with nonquaternary
belly allele jelly smelly deli telly underbelly vermicelli many messy heavy ready fairly rarely barely semi petty levy penny antennae heady levee medley unfairly jetty teddy bevy faery jenny kepi leggy recce sedgy veggie healthy steady wealthy deadly lengthy gentry unhealthy fleshy carefree sentry sexy sketchy spaghetti sweaty unsteady vestry belfry deathly gayety hefty machete confetti pebbly tempi testy breathy dressy pesky thready lefty wetly already directly especially twenty assembly scarcely elementary gently plenty epilepsy freshly immensely densely frenzy squarely deftly coquetry fleshly stealthy fidgety tensely trendy aplenty baronetcy libretti maidenly marquetry adeptly effendi ineptly friendly correctly complementary intensely intently unfriendly apoplexy halfpenny sullenly hostelry deviancy preciously woodenly indirectly incorrectly excellency complexly narcolepsy sacredly catalepsy reassembly penitently expressly confusedly equivalently grotesquely ambivalently cognoscenti circumspectly