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