multinyms are examples of triple/quadruple/quintuple/sextuple homonyms.

According to some definitions, a homonym is a word with the same pronunciation as, but different meaning than, another word. Thus, homonyms come in pairs (at least). However, some remarkable homonyms come in triples, as you may here behold.

Triplets:

• ade, aid, aide
• aisle, I'll, isle
• ait, ate, eight
• aye, eye, I
• axel, axil, axle
• bald, balled, bawled
• bases, basis, basses
  (distinguishable in careful speech.)
• beau, bo, bow
• bight, bite, byte
• bold, bolled, bowled
• bole, boll, bowl
• born, borne, bourn/bourne
• borough, burro, burrow
  (distinguishable in careful speech.)
• braise, brays, braze
• birr, bur, burr
• call, caul, col
• cedar, ceder, seeder
• ceiling, sealing, seeling
• censer, censor, sensor
• cent, scent, sent
• Chile, chili, chilly
• chord, cord, cored
• coal, cole, kohl
• coarse, corse, course
• coign, coin, quoin
• coward, cowered, cowherd
• dier, dire, dyer
• does, doughs, doze
  (does is the plural of doe, "a female deer")
• earn, erne, urn
• eaves, eves, Yves
• ewes, use, yews
• fain, fane, feign
• faro, farrow, pharoah
• firs, furs, furze
• flew, flu, flue
• for, fore, four
• frees, freeze, frieze
• gild, gilled, guild
• heal, heel, he'll
• hi, hie, high
• holey, holy, wholly
• idle, idol, idyll
  (idyll has a variant spelling "idyl" which we're not counting)
• knead, kneed, need
• knot, naught, not
• knows, noes, nose
• lade, laid, layed
• Lapps, laps, lapse
• lays, laze, leis
• liar, lier, lyre
• load, lode, lowed
• mead, Mede, meed
• meat, meet, mete
• mold, moled, mould
• mhorr, moor, more
• nay, nee, neigh
• pair, pare, pear
• palate, palette, pallet
• plainer, planar, planer
• polar, poler, poller
• poor, pore, pour
• prier, prior, pryor
• psis, sighs, size
  ("psi" is more properly pronounced "P-SEE" but then, we're not Greek so we can say it how we want to!)
• rain, reign, rein
• raiser, razer, razor
• rapped, rapt, wrapped
• read, rede, reed
• road, rode, rowed
• rood, rude, rued
• rheumy, roomie (a roommate), roomy
• roos, rues, ruse
  (roos is the plural of roo, a kangaroo)
• sacs, sacks, sax
• shier, shire, shyer
• sic, sick, Sikh
• sics, Sikhs, six;
• sign, sine, syne
• Sioux, sou, sue
• Sol, sole, soul
• sold, soled, souled
• taught, taut, tot
• their, there, they're
• to, too, two
• toad, toed, towed
• ton, tonne, tun
• vail, vale, veil
• vain, vane, vein
• vial, vile, viol
• wail, wale, whale
• ware, wear, where
• way, weigh, whey
• weal, we'll, wheel
• weather, wether, whether
• whined, wind, wined
• whys, wise, wyes

Quadruplets:

• adds, ads, adz, adze
• bi, buy, by, bye
• boar, Boer, boor, bore
  (distinguishable in careful speech. Thanks to Will Harrington for "Boer".)
• carat, caret, carrot, karat
• cees, seas, sees, seize
  (cees is the plural of cee which is a name for the letter "C" or the school grade, or any thing shaped like a "C").
• cense, cents, scents, sense
• cere, sear, seer, sere
• cinque, sink, sync, synch
• cite, cyte, sight, site
  (cyte is a mature germ cell)
• crews, cruise, crus, cruse
  (crus is the plural of cru, a French vineyard whose name is used to identify wine)
• dew, do, doux, due
  (doux is champagne that is at least seven percent sugar)
• eau, o, oh, owe
• ewe, yew, you, U
• gnu, knew, new, nu
  (American English; British English says 'knyew' and 'nyew', as pointed out by Warren Kinney.)
• heigh, hi, hie, high
• hoard, horde, hoared, whored
• mall, moll, maul, mawl
• medal, meddle, metal, mettle
  (distinguishable in careful speech.)
• oar, o'er, or, ore
• pairish, parish, pearish, perish
• peak, peek, peke, pique
• praise, prase, prays, preys
• rhos, roes, rose, rows
• right, rite, wright, write;
• teas, tease, tees, tis;
  (Here tis is meant as the plural of ti, a name for one step of the musical scale)
• wade, wayed, weighed, wheyed
• weald, wealed, wheeled, wield;

Quintuplets:

• seau, sew, so, soe, sow,
  (a seau is a "pottery pail" popularly used in 18th century table settings, but now on backorder;
  soe is a kind of large wooden tub,
  the sow we have here is the one meaning to plant)

Sextuplets:

• air, are, e'er, ere, err, heir

Septuplets:

• raise, rays, rase, raze, rehs, réis, res
  (rase is a verb meaning "to erase", rehs is the plural of reh, a mixture of sodium salts found as an efflorescence in India,
  réis is the plural of real, a currency unit of Portugal and Brazil,
  res is the plural of re, a name for one step of the musical scale)

Acknowledgements:

Thanks to Steve Schaefer for disqualifying "idyl", and for proposing the "medal/meddle/metal/mettle" quadruplet.

Thanks to Terry Stickels for sharing the results of her own research.

Thanks to David Norton for offering a number of new homonyms.

Thanks to Walton McNutt for the "their", "mall", "ton" and "taught" families.

Thanks to Carlos Augusto for correcting my explanation of réis.

Thanks to Warren Kinney for distinguishing the British pronunciation of "new" and "knew", and for suggesting that everyone knows that "tees" are those things you use in golf.