Highlighting the wider stakes, on Wednesday the United States Court of Appeals for the Fifth Circuit, overruling a lower court, said a Texas-style admitting-privileges law in Louisiana that is currently blocked should take immediate effect — which is likely to force three of the state’s four abortion clinics to close. Lawyers for the clinics said they would file an emergency appeal to the Supreme Court within days, arguing that the law should continue to be blocked while the justices consider whether such laws are constitutional.

On March 2, the Supreme Court is scheduled to hear arguments on the challenge to the Texas law, which requires abortion doctors to be affiliated with nearby hospitals and also limits abortion to ambulatory surgical centers. Abortion opponents say such measures are needed to protect women, but major medical groups say they will not enhance patient safety and will only reduce women’s access to abortion.

Overruling a lower court’s injunction, the Fifth Circuit appeals court allowed the Texas admitting-privilege rule to take effect throughout the state in 2013, immediately shuttering about half of what had been more than 40 abortion clinics, although exceptions were later granted for geographically isolated clinics in McAllen and El Paso. The second requirement, mandating costly surgical center facilities, has been temporarily stayed by the Supreme Court, but it would force still more reductions if upheld.

At stake in the case, Whole Woman’s Health v. Hellerstedt, is not only the future of abortion access in Texas and in the nine other states that, like Alabama and Louisiana, have adopted similar physician rules. It could also affect dozens of other regulations of disputed medical value that have been adopted by numerous states, including limits on nonsurgical drug-induced abortions, mandated building standards for clinics and two-day or three-day waiting periods.