During arguments on Louisiana’s abortion law Wednesday, Justice Samuel Alito Jr. appeared ready to reexamine a decades-long line of U.S. Supreme Court cases allowing individuals to raise the rights of others in challenges to allegedly unconstitutional law. But in all such challenges or just abortion cases?

Alito questioned Julie Rikelman of the Center for Reproductive Rights, counsel to the Louisiana clinic June Medical Services and its physicians, about one of the most potentially significant issues in the case: whether the clinic and physicians have so-called third-party standing to challenge the state’s hospital admitting privileges requirement. A ruling that they don’t have standing to sue could reduce or eliminate challenges to state abortion restrictions, according to abortion rights advocates.