Green’s Dictionary of Slang

corporation n.

[play on alderman n. (4)]

the body or stomach, esp. when fat.

Smollet Count Fathom (1813) I 156: Sirrah! my corporation is made up of good wholesome English fat; but you are puffed up with the wind of vanity and delusion.
[UK]Memoirs of the celebrated Miss Fanny M-. 129: He was fat enough to perform any part that did not require such a corporation as Sir John Falstaff.
[UK]Grose Classical Dict. of the Vulgar Tongue n.p.: Corporation, a large belly. He has a glorious corporation; he has a very prominent belly.
[UK]Sporting Mag. Apr. IV 52/2: The great rotundity of his shape, which affords his legal acquaintance cause for calling him a corporation sole.
[UK]Lex. Balatronicum.
[UK]Egan Anecdotes of the Turf, the Chase etc. 130: He appeared to me, a heavy, thick, round-made, large-boned man [...] he was in the vale of years, and had acquired some corporation.
[UK]Navy at Home II 185: Billybuffer was compared to a rum-puncheon, and from said rotundity, [...] being frequently, with faces of concern and condolence, asked after the health and state of his corporation.
[US]Ely’s Hawk & Buzzard (NY) Sept. 6 n.p.: Her corporation drawn in and her stern bulged out.
[US]Whip & Satirist of NY & Brooklyn (NY) 6 Aug. n.p.: We should judge from the appearance of her corporation that it [i.e. the subject’s income] is rather lean.
[UK]C. Brontë Shirley 375: The Rector [...] looming large in full canonicals [...] with the dignity of an ample corporation .
[UK]Fights for the Championship 112: Carter was also in robust health, but his corporation partook a little too much of civic importance.
[Ind]Delhi Sketch Bk 1 Mar. 26/2: It is a sight to [...] behold him drink, to watch the good liquor poured into his capacious corporation.
[UK]Hotten Dict. of Modern Sl. etc.
[UK]E. de la Bédollière Londres et les Anglais 313/2: corporation, corpulence.
[UK]Sl. Dict.
[UK]Sporting Times 30 Aug. 4/5: Shan’t want a chair, but a good broad sofa adapted to a decent [...] corporation.
W.P. Frith Autobiog. i 49: Very stout men... each possessing larger corporations than are commonly seen [F&H].
[Aus]Dead Bird (Sydney) 29 Mar. 2/2: Kearney was very stout and [...] to diminish the width of his target he tried to tuck in his corporation, and by doing so increased his protuberance behind.
[UK]Hunter & LeBrunn [perf. George Robey] ‘A B ab’ 🎵 To africa he went to show his half a ton of jelly, / [...] / he started off to Mr Rhodes, his corporation made two loads,.
[Aus]‘Miles Franklin’ My Brilliant Career 167: Two stout old squatters with big laughs and bigger corporations.
[Aus]E. Dyson ‘Dukie M’Kenzie’s Dawnce’ in Benno and Some of the Push 44: Cilly gave the wheel another turn, and a hard jet bounced off Jumbo’s large, taut corporation.
[US]Z.N. Hurston Gilded Six-Bits (1995) 988: He ain’t puzzle-gutted, honey. He jes’ got a corporation.
[UK]R. Llewellyn None But the Lonely Heart 70: He was only a little bloke, but broad as a door, with a corporation as made him leave the top three buttons of his trousers undone.
[UK]Guardian 4 July 🌐 Deparideu arrived last Friday. You can hardly miss him. He is a kenspeckled figure, about seven feet tall with a proportionate corporation.

SE in slang uses

In compounds

corporation cocktail (n.) [although in an age of natural gas this drink is redundant]

coal gas bubbled through milk, a down-and-out alcoholic’s tipple.

[UK]S. McConville ‘Prison Language’ in Michaels & Ricks (1980) 526: If all else fails, a buzz may be obtained by the down and out’s standby, the corporation cocktail, which is coal gas inhaled through milk.
corporation hair-oil (n.)

(Irish) water, as used in smoothing down the hair.

[UK]I. & P. Opie Lore and Lang. of Schoolchildren (1977) 184: Water is [...] widely referred to as ‘juice’, or ‘Corporation pop’. And ‘Corporation hair-oil’ is the commodity with which they (sometimes) flatten their hair of a morning.
[Ire]B. Quinn Smokey Hollow 51: He was the first to use ‘Corporation hairoil,’ or water, to achieve a quiff in his hair and was called a mickeydazzler because of it.