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