Here's what rhymes with posthigh.
high thy vi hi shy sigh fi hy thigh vie psi hai cy fy sy thei phi by my why die lie y buy fly sky guy tie bi bye chi dye nigh pi pie spy thai dei fry ly quae rye sly ty wir awry lye mai muy nai pacify wry kai lai luy mei tai wai sty bonsai ossify stye turfy banzais slier dry try cry justify defy ply pry tri trie pri deify spry scurfy barfly shanghai apply supply thereby deny rely satisfy hereby modify specify classify testify verify butterfly certify alibi diversify nullify ratify belie decry falsify pupae termini terrify typify untie descry edify mollify overlie ramify vilify aquae firefly vivify amebae blowfly calcify horrify stupefy lanai overfly versify mummify beatify drachmai overbuy dandify yuppify reply imply nearby occupy whereby qualify alkali signify glorify goodbye gratify notify purify underlie amplify fortify magnify samurai standby unify beautify lullaby amoebae codify crucify dignify mortify personify acidify detoxify mystify retry stratify stultify triply ultrahigh emulsify petrify dissatisfy scarify declassify prettify vitrify ripply speechify identify clarify comply nuclei simplify intensify quantify alveoli rectify solidify liquefy oversupply resupply demystify dragonfly misapply reclassify reunify revivify liquify hyperbolae gentrify refortify syllabify stimuli multiply disqualify indemnify objectify electrify preoccupy solemnify exemplify cumuli oversimplify misidentify transmogrify