Joining McCollum in the initial suit filed last month were attorneys general from South Carolina, Nebraska, Texas, Utah, Alabama, Colorado, Michigan, Pennsylvania, Washington, Idaho, and South Dakota, all Republicans; and Louisiana's Buddy Caldwell, a Democrat.
A hearing is set for April 14 in Pensacola.
Critics of the suit have dismissed it as groundless, and a political stunt designed to take advantage of public angst over the issue during an election year.
Several attorneys general who joined the suit are also running for governor, including McCollum, Terry Goddard, the Democratic attorney general of Nevada, and Greg Zoeller, the Republican attorney general from Indiana.
Republican lawmakers in Georgia additionally have threatened to impeach Democratic Attorney General Thurbert Baker, because he refused Republican Gov. Sonny Purdue's request to join the suit.