The Indiana Chamber of Commerce wants the state schools superintendent to be appointed by the governor in 2016, setting the stage for another acrimonious education battle.
In addition, the chamber said Monday it would back legislation lifting the state's law against carryout alcohol sales at grocery stores and other retailers.
Chamber President Kevin Brinegar said Monday that if lawmakers reject the education proposal, the governor's appointees on the State Board of Education should be allowed to elect a new chairman.
The board has been the arena for ardent fighting between Indiana Superintendent of Public Instruction Glenda Ritz, a Democrat, and Republicans. A walkout and lawsuit last year prompted U.S. Education Secretary Arne Duncan to deride Indiana's deep "dysfunction."
Republican legislative leaders have previously been apprehensive about stoking fights between Ritz and Republican Gov. Mike Pence.
Senate President Pro Tem David Long and Republican House Speaker Brian Bosma were scheduled to talk to the state chamber later Monday.
Meanwhile, Brinegar said Rep. Tom Dermody, chairman of the House Public Policy committee, planned to author legislation lifting the Sunday alcohol ban.