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