2 letters:
at

3 letters:
bat, cat, dat, fat, gat, 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, 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, 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, torchat, to that, traumat, urstadt, weechat, werecat, whereat, wildcat, winefat, wink at, work at, yediyat, zermatt, zikurat

8 letters:
achromat, aegrotat, aerostat, 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, firebrat, floormat, fruitbat, gyrostat, hell-cat, hemostat, 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, placemat, pluck at, pneumat-, prevatte, prostat-, pussycat, pyrostat, quail at, reformat, rheocrat, rice rat, ronstadt, roof rat, run-flat, sand cat, sand rat, schmatte, semarnat, shine at, 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, 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, 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, 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, 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, bristle at, bureaucrat, calico cat, cobicistat, concinnate, connive at, cotton rat, 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, serhetabat, 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, microformat, miner's cat, monochromat, opossum rat, panther cat, persian cat, priya bapat, rat-tat-tat, scaredy-cat, shammuramat, siamese cat, splintercat, spotted bat, tit-for-tat, tit for tat, vampire bat, verhofstadt, welcome mat

12 letters:
aufsichtsrat, autoexec.bat, bacteriostat, baseball bat, bell the cat, blepharostat, buffalo gnat, 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