3 syllables:
ybor city

4 syllables:
adversity, diversity, 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, circuitry, carelessly, urgency, surlily, courtesy, scornfully, organdy, fearfully, earnestly, purposely, artfully, artlessly, normally, tirelessly, garganey, dirtily, forcefully, verdancy, cheerfully, wordily, harmlessly, certainly, gorgeously, wordlessly, 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, artistry, churlishly, furtively, garlicky, garnishee, guardedly, learnedly, mercifully, mortgagee, perfidy, piercingly, scarcity, sparsity, sportingly, surgically, turgidly, twirlingly, varsity, yearningly

4 syllables:
infernally, commercially, enormously, eternally, deservedly, divergency, informally, importantly, enormity, discordantly, uncertainty, insurgency, conversancy, absorbency, emergency, observably, fraternity, deformity, internally, reportedly, acerbity, externally, convergency, hyperbole, disharmony, detergency, absurdity, advertency, conformity, remarkably, remorsefully, personally, eternity, maternally, conservancy, modernity, uncertainly, east germany, grand larceny, observantly, accordingly, assertively, discursively, divertingly, imperfectly, infirmity, lethargically, light-heartedly, maternity, observingly, paternity, unsportingly

5 syllables:
inadvertency, determinedly, proportionally, mysteriously, petit larceny, nonconformity, uniformity, controversially, universally, petty larceny, inadvertently, topsy-turvily, unassertively

6 syllables:
counterinsurgency