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