3 syllables:
ybor city

4 syllables:
adversity, dispersity, inter city, l-diversity, perversity, vniversity

5 syllables:
multiversity, university, wikiversity

6 syllables:
biodiversity, neurodiversity, polydispersity, yale university

7 syllables:
anna university, cambridge university, city university, harvard university, monsters university, oxford university, princeton university, stanford university

8 syllables:
brigham young university, texas a&m university, tsinghua university

10 syllables:
arizona state university

3 syllables:
normalcy, forename, certainty, partially, burgundy, larceny, cordially, sparsity, cursedly, circuitry, carelessly, urgency, surlily, artistry, sordidly, sportingly, courtesy, scornfully, organdy, fearfully, scarcity, earnestly, purposely, yearningly, concernedly, varsity, artfully, learnedly, artlessly, mortgagee, churlishly, furtively, normally, guardedly, perfidy, tirelessly, garganey, dirtily, forcefully, verdancy, cheerfully, garnishee, wordily, turgidly, garlicky, harmlessly, certainly, gorgeously, wordlessly, torpidly, markedly, fearlessly, heartily, scurvily, stormily, carpentry, perfectly, harlotry, harmony, urgently, dormancy, tardily, forcibly, pharmacy, fervently, servilely, carefully, organdie, fervency, harmfully, argosy, formally, normandy, archduchy, germany, thirstily, carnegie, cheerlessly, chirpily, earthnut pea, fervidly, fort-lamy, jerkily, marquetry, mirthfully, nervelessly, nervily, normandie, perkily, smarmily, verdandi, piercingly, twirlingly

4 syllables:
infernally, imperfectly, commercially, enormously, eternally, deservedly, infirmity, divergency, informally, importantly, enormity, accordingly, lethargically, discordantly, uncertainty, insurgency, assertively, quaternity, conversancy, absorbency, emergency, maternity, observably, paternity, fraternity, deformity, internally, reportedly, discourtesy, acerbity, externally, convergency, hyperbole, disharmony, detergency, absurdity, advertency, conformity, remarkably, discursively, remorsefully, personally, eternity, maternally, mercifully, conservancy, modernity, uncertainly, surgically, east germany, grand larceny, observantly, abnormalcy, advertently, basse-normandie, cryptorchidy, haute-normandie, in harmony, remorselessly, transversally, white burgundy, with courtesy, divertingly, light-heartedly, observingly, unsportingly

5 syllables:
inadvertency, determinedly, proportionally, mysteriously, petit larceny, nonconformity, taciturnity, uniformity, controversially, universally, petty larceny, inadvertently, andrew carnegie, lower-normandy, most importantly, nonabsorbency, undeservedly, unremarkably, upper-normandy, topsy-turvily, unassertively

6 syllables:
counterinsurgency, musical harmony, nonuniformity, uncontroversially

10 syllables:
federal republic of germany