The Power Four conferences are attempting to stop NFL players and other professionals from becoming college athletes again, but they’ll likely need to convince federal and state courts that banning former (and perhaps future) pros is lawful under antitrust law.

Media reports on Tuesday indicate that the Big Ten, SEC, Big 12 and ACC are weighing—and will likely approve—new eligibility rules distinct from existing NCAA eligibility rules that deem ineligible players who declare for the NFL Draft and don’t withdraw, or who take further steps, such as signing a contract with an NFL team.

Such rulemaking would conflict with the return of players like tight end Dae’Quan Wright, whom the Cleveland Browns waived this week so that he could sign with LSU following a ruling by a Louisiana judge permitting Wright and other players to return.

It’s possible these conferences will also disallow basketball players who sign with NBA teams, such as new LSU player RJ Luis Jr.; he was previously under contract with the Utah Jazz and Boston Celtics and played in the NBA preseason.

The eligibility of players who are seasoned college athletes, some of whom turn pro and then want to come back, has become a major legal controversy in the sports industry and obscured the line between college and professional.