Green’s Dictionary of Slang

modified by any suitable v., to a (very) great extent; see blow up a storm v., cook up a storm under cook up v., piss up a storm under piss v., talk up a storm under talk v.

1960		‘Lord Buckley’ Hiparama of the Classics 21: Nero is havin’ a ball, he’s diggin’ this mad game, he’s juicin’ up a storm, chompin’ on his crazy pills.
1971		P. Foster Pops Foster 171: Marty and I were drinking up a storm that night and we kept passing glasses of whiskey up to the boat pilot all night.
1976		J. Hayes ‘Gayspeak’ Quarterly Journal Speech LXI 256–66: In his white levis and jacket just posing up a storm.
1990		(con. early 1950s) J. Ellroy L.A. Confidential 154: Waiting for him: Breuning, two hooker types – laughing up a storm in the sweatbox.
2003		G. Tate Midnight Lightning 4: His own mad children can’t ever stop themselves from cussing up a storm.