More than half the nation’s attorneys general want the Supreme Court to revisit the Affordable Care Act in the coming months.

Attorneys general in 29 states urged the court in filings this week to review lower-court decisions on the landmark health care law’s contraception mandate, but they were split over which of two cases the court should focus on. Both involve employers who say the law’s contraception mandate violates their freedom of religion.

Eleven attorneys general, along with the White House, want the court to review a lower-court opinion that found that the contraception mandate violates a business’s freedom of religion. Eighteen other state attorneys general want the court to review another opinion, which found the opposite. Dozens of lawsuits on that mandate have been filed by nonprofits and corporations nationwide.

“This isn’t necessarily an easy question with an easy answer,” says South Dakota Attorney General Marty Jackley, who joined the 17 attorneys general seeking a review of the ruling that upheld the law’s contraception mandate. “In other words, each side can cite supporting authority for their positions, which is why in and of itself it’s important for the Supreme Court to solve this.”

Those 18 states, led by Ohio and Michigan, want the court to review a Third Circuit Court of Appeals ruling that upheld the mandate, which covers contraception that includes the morning-after pill. In that case, the Mennonite Hahn family of Pennsylvania, owners of the kitchen cabinet part manufacturer Conestoga Wood Specialties, sued the U.S. Department of Health and Human Services, arguing that the law’s mandate violated their religious beliefs.

But the case has implications beyond just the mandate, Jackley says.

“At least from my perspective, it’s bigger than that,” he says. “The question is can a federal mandate force upon an individual or businesses something that is contrary to their religious beliefs? And I believe that is something that the First Amendment protects against.”

Another case — in which the court found the mandate did violate a firm’s religious expression—may also have far-reaching implications, California Attorney General Kamala Harris argued in the separate filing with 10 other state attorneys general.

In that case, the Green family, which owns the nationwide Hobby Lobby arts and crafts chain of stores, sued the government just as the Hahn family had. The Tenth Circuit Court of Appeals sided with the family in June, arguing that the contraception requirement violates the religious rights of the Christian family and its businesses.

California and the other states see a few big problems with that decision: It grants broad powers to corporations, restricts employee rights and limits states’ power to protect public health and gender equity in health care access. There are also other complications, such as how to determine a corporation’s religious views.

“[H]ow should a court determine the religion of a corporation where a minority of owners or shareholders does not share the religious views of the majority? Or where shareholders disagree on the obligations imposed by their commonly-held religion?” the states ask in their filing.

If that ruling is upheld, the attorneys general argue, businesses could claim religious exemptions to all sorts of state and federal regulations in the areas of public safety, civil rights, social welfare, land use, housing, employment and public health.

Harris was joined by the attorneys general from Connecticut, Hawaii, Illinois, Iowa, Maine, Maryland, New York, Oregon, Vermont and Washington.

Jackley was joined by his counterparts in Alabama, Alaska, Colorado, Florida, Georgia, Idaho, Kansas, Louisiana, Michigan, Montana, Nebraska, Ohio, Oklahoma, South Carolina, Texas, Virginia and West Virginia.