The highly selective university faces funding threats from the Trump administration along with rising costs and proposed policy changes.
In a court filing Friday, the colleges argued that the elimination of Harvard's federal funding "negatively impacts the entire ecosystem."
The measures come amid widespread reports of scammers using financial aid applications to steal both federal and state money.
If passed, the bill would create the Ohio Civics Board and give the centers' current directors oversight of the selection of their successors.