COLUMBUS, Ohio — A state inquiry in Ohio into allegations of misconduct inside Concept Schools, the embattled charter-school chain based in Des Plaines, has been expanded to two additional cities.

The Ohio Department of Education already was investigating a Dayton-area Horizon Academy, run by Concept, after teachers there told in July of sex games, test-tampering and other potentially criminal misdeeds.

Spokesman John Charlton said Tuesday that, after that meeting, Ohio state authorities received additional complaints about schools in Columbus and Cincinnati run by the same operator.

Both of the complaints were against Horizon Science academies run by Concept, Charlton said. One was unsolicited, and the other resulted from a department request that any issues at the schools be brought to authorities’ attention.

Separately, the FBI has been investigating Concept charter schools in Ohio and several other states, including Illinois. The FBI raided Concept’s headquarters in Des Plaines in June. FBI officials have declined to say what they’re investigating.

Salim Ucan, a Concept Schools vice president, said the company was unaware until Tuesday that additional complaints had been added to the Ohio review.

“We will definitely look into them and take it seriously, as we have in the past with all of these other allegations,” Ucan said.

Officials at a Cleveland school also have been questioned.

Charlton said the complaints have been referred to the appropriate regions for further review.

“What we did with those complaints or allegations was we matched them up with the appropriate office at their Department of Education, where they’ve contacted teachers and others for more specific information,” he said.

Charlton said those referrals aren’t part of a formal investigation.

News of the expanded review came as an estimated 400 supporters of Horizon and Noble academies were in Columbus to rally at the Ohio Statehouse and testify before the state school board.

Blue Ribbon Friends, the coalition of parents, teachers and other supporters of the academies, organized the events. A spokesman said the group believes issues at Concept Schools are being used by charter-school opponents, including teacher unions.

“Our parents are here to let their voice be heard, that there may be a few former teachers complaining and bringing up the allegations and accusations, but there are hundreds more — if not thousands more — who could share the opposite of what’s been presented and portrayed over the last few months,” Ucan said.

Among them was Olivia Reine, whose grandson attends the Horizon Academy in Dayton. “I like what I see,” Reine said of the school.