2 letters:
at

3 letters:
bat, cat, dat, fat, gat, hat, kat, mat, nat, pat, rat, sat, tat, vat

4 letters:
batt, brat, catt, chat, elat, flat, gatt, gnat, hatt, hnat, jagt, katt, krat, matt, patt, scat, slat, spat, stat, that

5 letters:
-crat, -stat, annat, arhat, ariat, asiat, assat, aviat, batte, begat, bhatt, blatt, borat, bratt, catte, cemat, cepat, cerat, citat, decat, defat, domat, ducat, eclat, eilat, empat, esbat, estat, exfat, expat, flatt, glatt, gnatt, hacat, hatte, hepat, hesat, iccat, ichat, incat, insat, intat, jatte, klatt, korat, kratt, legat, lstat, ma'at, matte, mofat, motat, natte, njrat, nopat, optat, orbat, patte, platt, popat, porat, pratt, ratte, rstat, sadat, satte, scatt, scrat, sebat, shatt, sifat, silat, skatt, slatt, socat, somat, splat, sprat, statt, strat, susat, tapat, tomat, tratt, tvsat, uncat, unhat, wesat

6 letters:
a-flat, abitat, acupat, airbat, al-lat, aparat, arnatt, aromat, at-bat, b-flat, bigfat, blatte, bobcat, bogmat, buy at, cadpat, caveat, cavtat, cerat-, chatte, climat, combat, commat, comrat, comtat, cowpat, cuecat, d'etat, diktat, dorpat, eat at, ex-pat, explat, farhat, fatcat, fltsat, format, get at, gfycat, gujrat, haemat, hazmat, heirat, hepat-, hepcat, hereat, hikmat, impatt, instat, iostat, jorhat, karjat, khilat, kismat, kitcat, labatt, lestat, limbat, lokmat, lolcat, mancat, marpat, matpat, mcnatt, mentat, mercat, mudcat, nadsat, navsat, netcat, nonfat, noplat, numbat, ocicat, pitpat, platte, pratte, qismat, redcat, redhat, rugrat, sabbat, sairat, sarsat, schadt, seacat, sehcat, sigcat, slaght, specat, splatt, spratt, therat, tipcat, tomcat, topcat, tschat, unimat, unplat, verrat, vrchat, wombat, youcat, ziarat

7 letters:
acrobat, adigrat, aerobat, akkurat, akrobat, antifat, apitpat, apparat, automat, babysat, bad hat, balyeat, batibat, bearcat, beermat, biernat, big cat, bougnat, bullbat, call at, castrat, chip at, chromat, cluebat, cocomat, combate, comstat, copycat, debatte, delatte, dingbat, displat, doormat, entheat, estedat, fat-cat, femstat, fittrat, forstat, fotomat, freemat, fur hat, gib-cat, gnaw at, gujarat, gujerat, habitat, hashcat, hellcat, hexchat, himavat, hipchat, hurlbat, in that, is that, jest at, keelfat, ketupat, kit-cat, kit-kat, kurdsat, landsat, langsat, latitat, look at, low-fat, man-bat, meercat, megabat, milkfat, minorat, moonbat, mudflat, muskrat, nilstat, non-fat, of that, on that, packrat, panipat, peck at, pick at, pitapat, play at, pneumat, poke at, polecat, prevatt, pulicat, pull at, rat-tat, red bat, reostat, saltcat, sarratt, sea mat, semimat, shmatte, shop at, snap at, sno-cat, snowcat, starsat, stay at, suricat, thereat, tib-cat, tin hat, top hat, torchat, to that, traumat, urstadt, weechat, werecat, whereat, wildcat, winefat, wink at, work at, yediyat, zermatt, zikurat

8 letters:
achromat, aegrotat, alleycat, amadavat, ameretat, amphicat, and that, assignat, autocrat, autokrat, autostat, avadavat, baby-sat, backchat, ballarat, bancomat, bankomat, barostat, bath mat, bear cat, blue cat, bone fat, brickbat, but that, camostat, cave bat, chauchat, chitchat, compumat, coon cat, cryostat, democrat, demokrat, deslatte, despotat, diplomat, doja cat, down pat, dth vsat, dutchbat, ekkathat, ergostat, ethercat, excel at, felt hat, firebrat, floormat, fruitbat, gyrostat, hard hat, hell-cat, hemostat, high hat, housecat, howeitat, inmarsat, inverlat, josaphat, karstadt, kattegat, kolovrat, laugh at, leaf fat, manx cat, microbat, mobocrat, mole-rat, mole rat, monistat, monocrat, mud flat, mule fat, musk-rat, orlistat, pack-rat, pack rat, palm cat, panamsat, pancreat, parmalat, pith hat, placemat, pluck at, plug hat, pneumat-, prevatte, prostat-, pussycat, pyrostat, quail at, reformat, rheocrat, rice rat, ronstadt, roof rat, run-flat, sand cat, sand rat, schmatte, semarnat, shine at, silk hat, smartcat, snapchat, standpat, stonecat, tablemat, theocrat, tinychat, true cat, velostat, whirlbat, wild-cat, wood-rat, woodchat, wood rat, wool fat, worldcat, ziggurat, zikkurat

9 letters:
al-adiyat, alley-cat, alley cat, andermatt, apostolat, arrive at, autostadt, a look at, ben platt, bierstadt, black cat, black rat, brass hat, bridle at, brown bat, brown rat, bundesrat, butterfat, carlstadt, chemostat, chit-chat, choueifat, civet cat, clam-flat, clarostat, clinostat, coelostat, cosmocrat, cryptocat, dabble at, darmstadt, dichromat, dixiecrat, does that, dress hat, eberstadt, eizenstat, erftstadt, fall flat, fantomcat, fruit bat, fungistat, gall gnat, guano bat, haemostat, hallstadt, house cat, hydrostat, hygrostat, hyperstat, judeo-tat, karlstadt, kattegatt, kitty-cat, klinostat, kompromat, lippstadt, mabalacat, marrowfat, monsarrat, nikkormat, nitrostat, noncombat, ochlocrat, opera hat, orthostat, pancreat-, photostat, pit-a-pat, pitty-pat, pizza rat, place mat, plutocrat, rampurhat, rat-a-tat, reichsrat, sam & cat, semimatte, sewer rat, shaktipat, shtrafbat, slavocrat, stand pat, straw hat, stripchat, such that, supayalat, superflat, tabby cat, table mat, thefatrat, tiger cat, tittlebat, trade rat, valued at, wall-plat, water mat, water rat, wharf rat, wikistrat, wing flat, with that

10 letters:
angora cat, animal fat, apochromat, aristocrat, aristokrat, beaver rat, bellingcat, bengal cat, bowler hat, bristle at, bureaucrat, calico cat, cobicistat, cocked hat, concinnate, connive at, cotton rat, cowboy hat, desert rat, dolcelatte, durrenmatt, edible fat, en-mishpat, febuxostat, festplatte, fisher cat, flying cat, fraidy-cat, gamarjobat, gornergrat, guerguerat, hauptstadt, humidistat, ingolstadt, jehosaphat, jungle cat, junooniyat, khubsoorat, kurzgesagt, laundromat, looking at, magnificat, marten cat, meritocrat, monstercat, montferrat, native cat, norway rat, orange bat, pallid bat, physiocrat, pocket rat, prayer mat, rosenblatt, roxadustat, safety hat, serhetabat, shovel hat, slouch hat, sphynx cat, superstrat, technocrat, thermostat, thundercat, trichromat, under that, vanderjagt, vorinostat, windirstat, wurstsalat

11 letters:
basel-stadt, become flat, burmese cat, cephalostat, channel cat, chris pratt, coup d'etat, cricket bat, data format, filderstadt, frosted bat, fungus gnat, gerontocrat, hognose bat, intercombat, jackass bat, leopard cat, maltese cat, mastiff bat, mexican hat, microformat, miner's cat, monochromat, opossum rat, panther cat, persian cat, picture hat, priya bapat, rat-tat-tat, scaredy-cat, shammuramat, siamese cat, splintercat, spotted bat, tit-for-tat, tit for tat, vampire bat, verhofstadt, welcome mat, woman's hat

12 letters:
aufsichtsrat, autoexec.bat, bacteriostat, baseball bat, bell the cat, bishop's hat, blepharostat, buffalo gnat, campaign hat, cavalier hat, chip away at, chow yun-fat, commissariat, domestic cat, egyptian cat, frankenstrat, hierogrammat, ilta-sanomat, kangaroo rat, large-format, leopoldstadt, masterformat, microhabitat, mutessarifat, north platte, oliver platt, pallas's cat, panobinostat, pocketed bat, potentiostat, raaz-e-ulfat, schallplatte, south platte, thalassocrat, vagharshapat, westerplatte

13 letters:
big brown bat, casey neistat, catheterostat, fort-la-latte, he's all that, horseshoe bat, marsupial rat, mortal combat, railroad flat, rat-a-tat-tat, wrestling mat

14 letters:
chinchilla rat, madagascar cat, naked mole rat, new world chat, old world chat, she's all that, wechselapparat, what does that

15 letters:
carnivorous bat, hesse-darmstadt, male aristocrat, reichskonkordat

16 letters:
blue channel cat, dilraba dilmurat, dwarf pocket rat, european wildcat, little brown bat, ord kangaroo rat, true vampire bat

17 letters:
alexandre desplat, false vampire bat, female aristocrat, florida water rat, tortoiseshell-cat

18 letters:
european brown bat, reichskommissariat

19 letters:
grumman f-14 tomcat, grumman f6f hellcat

20 letters:
orange horseshoe bat

21 letters:
and just like that...

22 letters:
palaeologus-montferrat, schwarzburg-rudolstadt

25 letters:
landkreuzer p. 1000 ratte

10 letters:
neuroblast