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