State Sen. Kevin Bacon, a Republican, said SB5 would also be amended to ban strikes by any state or local public employees, not just those in public safety, The Plain Dealer of Cleveland reported.
He said unions would be able to bargain only on wages.
Bacon heads the committee now dealing with the bill. As originally written, it ended collective bargaining for all state employees and binding arbitration for local government workers.
Senate President Tom Niehaus said Republicans are still working out details. Those include what would happen if public employee unions and government agencies cannot reach agreement.
"We are working on an alternative that would allow them to take their concerns to a third party," Niehaus said. "But it will not be binding arbitration."
More than 5,000 people rallied against the bill Tuesday in Columbus.