4 syllables:
integrity

5 syllables:
change integrity

6 syllables:
change of integrity

3 syllables:
benghazi, bestially, breathlessly, brevity, centrally, chemically, chemistry, clemency, credibly, density, deputy, desperately, destiny, devilry, dextrously, dreadfully, ebony, ecstasy, ectropy, elegy, embassy, emigree, empathy, endlessly, enemy, enmity, entity, entropy, equity, evilly, fecklessly, federally, felony, flexibly, gemini, generally, heavenly, heavily, helpfully, helplessly, jealously, jealousy, jejunely, kennedy, legacy, legatee, legibly, lemony, lengthily, lenity, leprosy, medically, melanie, melody, mentally, peasantry, pebbly, pedantry, pederasty, pedigree, penally, penalty, pleasantly, pleasantry, preciously, preferably, pregnancy, presently, readily, recipe, remedy, resiny, restfully, revelry, secondly, self-pity, selflessly, senselessly, sensibly, sentiency, separately, sesame, seventy, severally, specially, specialty, splendidly, steadily, stephanie, tenancy, tenantry, tendency, tensity, tentatively, tepidly, testily, threnody, trenchancy, trepidly, velvety, venally, vengefully, weaponry, yemeni, zealotry, zestfully, zestily

4 syllables:
intricacy, inclemency, intricately, impotently, criminally, impudently, intimacy, militancy, vigilantly, minimally, immanency, indecently, intimately, lycanthropy, infinitely, difficulty, immodestly, acceptably, acephaly, allegedly, amenity, anemone, ascendancy, ascendency, complexity, confederacy, confessedly, contemptuously, convexity, death penalty, defencelessly, dependency, detestably, discrepancy, domenici, especially, essentially, eventually, exceptionally, expectancy, extremity, fidelity, flux density, forelady, hegemony, heredity, identity, illegibly, immensity, impendency, impetuously, incessancy, incessantly, incredibly, indemnity, ineffably, inequity, infectiously, inflexibly, insensibly, intensity, intrepidly, jack kennedy, lamentably, licentiously, lieutenancy, lobectomy, longevity, low density, lumpectomy, mastectomy, necessity, nephrectomy, neurectomy, nonentity, ostensibly, penelope, perceptibly, perplexedly, perplexity, polemically, potentially, pretentiously, professedly, professionally, quiescency, rebelliously, refreshfully, regrettably, relentlessly, repentantly, respectably, respectfully, resplendency, resplendently, revengefully, schenectady, sententiously, sequentially, serenity, shell entity, solemnity, splenectomy, successfully, supremacy, telemetry, telepathy, thrombectomy, transcendency, tremendously, unhelpfully, unpleasantly, unsteadily, vasectomy, vulvectomy, with empathy

5 syllables:
precipitately, legitimately, inimitably, equivocally, legitimacy, conditionally, additionally, prolificacy, felicitously, originally, precipitancy, traditionally, ridiculously, reciprocally, articulately, magnificently, accidentally, acrocephaly, anencephaly, appendectomy, biochemistry, change intensity, clinocephaly, coalescency, conscientiously, consequentially, create mentally, deferentially, detrimentally, disrespectfully, drunken revelry, embolectomy, field intensity, fundamentally, geochemistry, half-intensity, high-fidelity, high fidelity, hydrocephaly, hysterectomy, incidentally, independency, independently, intumescency, laminectomy, laryngectomy, life expectancy, line of destiny, macrocephaly, mask of pregnancy, mastoidectomy, megacephaly, meniscectomy, microcephaly, mortal enemy, mountain ebony, nanocephaly, naval weaponry, of necessity, oophorectomy, open sesame, orchidectomy, orchiectomy, penitentially, photochemistry, pneumonectomy, prostatectomy, providentially, reprehensibly, reverentially, rhytidectomy, salpingectomy, scaphocephaly, school of dentistry, sentimentally, sigmoidectomy, stapedectomy, sympathectomy, thyroidectomy, tonsillectomy, tubal pregnancy, unacceptably, unforgettably, unintentionally, unpretentiously, unrepentantly, unsuccessfully, vapor density, white supremacy

6 syllables:
indiscriminately, unconditionally, illegitimacy, illegitimately, unequivocally, adenoidectomy, adrenalectomy, anas penelope, appendicectomy, cholecystectomy, coincidentally, cosmetic dentistry, electrochemistry, environmentally, experimentally, genus penelope, immunochemistry, inconsequentially, interdependency, manifest destiny, militant tendency, organic chemistry, ovariectomy, panhysterectomy, pedal extremity, physical chemistry, radiochemistry, relative density, simple mastectomy, unsentimentally

7 syllables:
abdominal pregnancy, department of chemistry, executive clemency, feeling of identity, inorganic chemistry, john fitzgerald kennedy, magnetic flux density, magnetic intensity, ovarian pregnancy, radical mastectomy, suprarenalectomy, total hysterectomy

8 syllables:
conformational entropy, interpersonal chemistry, radical hysterectomy

10 syllables:
modified radical mastectomy