Based on the file web2 from a NeXT machine, here are some words, I suppose, that form a chain of seven anagrams:

• able, albe, bale, beal, bela, blae, Abel
• agnel, angel, angle, genal, glean, lagen, Galen
• agroan, arango, onagra, Onagra, Angora, Anogra, Argoan
• alban, banal, nabla, Nabal, Laban, Balan, Alban
• albeit, albite, baltei, betail, libate, Belait, Bletia
• aldern, darnel, enlard, lander, lenard, randle, reland
• aldine, denial, enalid, leadin, Daniel, Delian, Aldine
• alen, lane, lean, nael, neal, Neal, Lena
• alert, alter, artel, later, ratel, taler, telar
• alien, anile, elain, laine, linea, Elian, Aline
• amen, enam, mane, mean, name, nema, Amen
• ante, etna, neat, taen, tane, tean, Aten
• antu, aunt, naut, taun, tuan, tuna, Antu
• argel, ergal, garle, glare, lager, large, regal
• arpent, enrapt, entrap, panter, parent, pretan, trepan
• atle, laet, late, leat, tael, tale, teal
• canter, creant, nectar, recant, tanrec, trance, Cretan
• darter, dartre, redart, retard, retrad, tarred, trader
• dater, derat, detar, drate, rated, trade, tread
• emir, mire, reim, riem, rime, Remi, Imer
• enol, leno, lone, noel, Noel, Leon, Elon
• entrail, latrine, ratline, reliant, retinal, trenail, Latiner
• inset, neist, snite, stein, stine, tsine, Stein
• least, setal, slate, stale, steal, stela, tales
• lepra, paler, parel, parle, pearl, relap, Perla
• mate, meat, meta, tame, team, Tame, Tema
• sart, star, stra, tars, tsar, Sart, Star
• sawt, staw, swat, taws, twas, wast, Swat

Chains of eight anagrams:

• acrolein, arecolin, caroline, colinear, creolian, Lonicera, Caroline, Cornelia
• alem, alme, lame, leam, male, meal, mela, Male
• aril, lair, lari, liar, lira, rail, rial, Lari
• arist, astir, sitar, stair, stria, tarsi, tisar, Trias
• armet, mater, metra, ramet, tamer, terma, trame, Trema
• easting, gainset, genista, ingesta, seating, signate, teasing, Genista
• laster, lastre, rastle, relast, resalt, salter, slater, stelar
• leapt, palet, patel, pelta, petal, plate, pleat, tepal

Chains of nine anagrams:

• acinar, arnica, canari, carina, crania, narica, Canari, Carian, Crania
• asteer, easter, reseat, saeter, seater, staree, teaser, Easter, Eastre
• caret, carte, cater, crate, creat, creta, react, recta, trace
• ester, estre, reest, reset, steer, stere, stree, terse, tsere

Chain of ten anagrams:

• lapse, salep, saple, sepal, slape, spale, speal, Pales, Lepas, Elaps

Chain of eleven anagrams:

• angor, argon, goran, grano, groan, nagor, orang, organ, rogan, Ronga, Orang

One-word anagrams with more than fifteen letters:

• acetmethylanilide, methylacetanilide
• anatomicopathologic, pathologicoanatomic
• anatomicopathological, pathologicoanatomical
• anatomicophysiologic, physiologicoanatomic
• antibenzaldoxime, benzantialdoxime
• arthrochondritis, chondroarthritis
• autoradiographic, radioautographic
• basiparachromatin, Marsipobranchiata
• biopsychological, psychobiological
• calcareocorneous, corneocalcareous
• calcareosiliceous, siliceocalcareous
• cephalomeningitis, meningocephalitis
• cerebromeningitis, meningocerebritis
• chemicomechanical, mechanicochemical
• cholecystoduodenostomy, duodenocholecystostomy
• chondromyxosarcoma, myxochondrosarcoma
• chorioidoretinitis, retinochorioiditis
• chromolithography, lithochromography
• chromophotography, photochromography
• chromophotolithograph, photochromolithograph
• chronophotograph, photochronograph
• chronophotographic, photochronographic
• chronophotography, photochronography
• clinicopathological, pathologicoclinical
• configurationism, misconfiguration
• constitutionalism, misconstitutional
• dioeciopolygamous, polygamodioecious
• duodenopancreatectomy, pancreatoduodenectomy
• dynamoelectrical, electrodynamical
• electromagnetical, magnetoelectrical
• electrothermometer, thermoelectrometer
• encephalomeningitis, meningoencephalitis
• encephalomeningocele, meningoencephalocele
• encephalomyelitis, myeloencephalitis
• epididymovasostomy, vasoepididymostomy
• esophagogastrostomy, gastroesophagostomy
• ferrihydrocyanic, hydroferricyanic
• ferrohydrocyanic, hydroferrocyanic
• fibromyxosarcoma, myxofibrosarcoma
• galvanothermometer, thermogalvanometer
• glossolabiolaryngeal, labioglossolaryngeal
• glossolabiopharyngeal, labioglossopharyngeal
• glycerophosphate, phosphoglycerate
• heliophotography, photoheliography
• hemopneumothorax, pneumohemothorax
• hexakisoctahedron, octakishexahedron
• hexakistetrahedron, tetrakishexahedron
• hydropneumopericardium, pneumohydropericardium
• hydropneumothorax, pneumohydrothorax
• hysterolaparotomy, laparohysterotomy
• hysteromyomectomy, myomohysterectomy
• incontrovertibility, introconvertibility
• incontrovertible, introconvertible
• intestinovesical, vesicointestinal
• laparosplenotomy, splenolaparotomy
• laryngopharyngeal, pharyngolaryngeal
• laryngopharyngitis, pharyngolaryngitis
• laryngotracheotomy, tracheolaryngotomy
• lithophotography, photolithography
• meningomyelocele, myelomeningocele
• microphotographic, photomicrographic
• microphotography, photomicrography
• microspectroscope, spectromicroscope
• misrepresentation, representationism
• monopersulphuric, permonosulphuric
• neuropsychological, psychoneurological
• occipitotemporal, temporooccipital
• parietosquamosal, squamosoparietal
• pectinatopinnate, pinnatopectinate
• pericardiacophrenic, phrenicopericardiac
• pericardiopleural, pleuropericardial
• petrographically, pterylographical
• pharyngorhinitis, rhinopharyngitis
• photostereograph, stereophotograph
• phototelegraphic, telephotographic
• physiopsychological, psychophysiological
• physiopsychology, psychophysiology
• psychotechnology, technopsychology
• pyeloureterogram, ureteropyelogram
• sacculoutricular, utriculosaccular
• somatosplanchnic, splanchnosomatic
• spectrotelescope, telespectroscope
• streptothricosis, streptotrichosis

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