3 syllables:
aleksey, aleksi, aleksy, galaxie

4 syllables:
agalaxy

5 syllables:
antigalaxy, metagalaxy, protogalaxy, supergalaxy

3 syllables:
happily, fractiously, gallantly, thankfully, tapestry, axletree, phantasy, cabinetry, capably, scammony, apogee, chastity, nastily, blasphemy, anthony, sanity, craftily, cavity, banditry, tragedy, balcony, rampantly, gascony, balmily, gravelly, captaincy, travesty, fallacy, gravity, patchouli, nascency, stagnancy, damnably, rapidly, laxity, bashfully, halfpenny, apathy, satiny, faculty, calumny, valiantly, valency, ataxy, abbacy, absently, antony, lazily, baptistery, atrophy, amnesty, majesty, callously, mangabey, maggoty, scantily, practically, anxiously, anomie, angrily, flashily, cadency, gallantry, agony, rhapsody, falconry, sassaby, agilely, scrappily, tangency, bankruptcy, passably, saxony, patently, tammany, gadgetry, fantasy, valiancy, malady, family, pageantry, handily, tastily, basketry, cannily, manfully, tactfully, alchemy, plangency, randomly, canopy, affably, manatee, cavalry, vanity, rackety, strategy, rascally, agassi, baptistry, cagily, chaplaincy, chattily, dapple-grey, dappled-grey, faddily, jaggedly, lambency, laughably, laxly, mccabe, natalie, pallidly, raggedly, ratafee, sacristy, scrabbly, tactlessly, tattily, wackily

4 syllables:
tonality, modality, casually, formality, vitality, unhappily, brutality, concavity, depravity, rationally, fugacity, casualty, actually, opacity, diastole, alacrity, sagacity, compatibly, mentality, catastrophe, audacity, mortality, anatomy, locality, nasality, substantially, naturally, vivacity, mammalogy, calamity, neutrality, edacity, frugality, legality, pugnacity, insanity, philately, totality, analogy, elaborately, disassembly, academy, profanity, nationally, lethality, juglandaceae, rapacity, reality, anastrophe, capacity, normality, sodality, finality, carnality, philanthropy, morality, examinee, salacity, voracity, financially, dextrality, inanity, loquacity, rascality, unmanfully, urbanity

5 syllables:
sexuality, cordiality, perspicacity, triviality, understandably, actuality, factuality, unreality, criticality, abnormality, circumstantially, incapacity, joviality, alismatidae, pertinacity, subnormality, geniality, satisfactorily, liberality, nationality, practicality, commonality, hylobatidae, inhumanity, irrationally, hospitality, underhandedly, animality, sensuality, generality, musicality, unnaturally, partiality, clinodactyly, corporeality, incompatibly, irreality, logicality, lyricality, physicality, prodigality, sesquipedality, severality, sinistrality, spatiality, temporality, typicality, verticality, whimsicality

6 syllables:
asexuality, araliaceae, incorporeality, congeniality, unilaterally, bilaterality, universality, irrationality, spirituality, substantiality, amaranthaceae, ambystomatidae, bisexuality, municipality, internationally, dimensionality, artificiality, aerophilately, atypicality, conviviality, cylindricality, ephemerality, essentiality, horizontality, illiberality, illogicality, impracticality, neuroanatomy, nonsensicality, polytonality, potentiality, reciprocality, theatricality, unsatisfactorily, untypicality, ununderstandably

7 syllables:
superficiality, homosexuality, insubstantiality, immateriality, territoriality, confidentiality, inessentiality, one-dimensionality, psychosexuality, third-dimensionality, three-dimensionality, two-dimensionality, uncongeniality