Read more of our coverage on challenges to the Affordable Care Act’s birth control benefit here.

Lawyers representing Priests for Life and other religiously affiliated nonprofits told a federal appeals court Tuesday that nothing short of extending the full exemption from the Affordable Care Act’s contraception coverage requirement would be enough to satisfy the religious objections of their clients.

The statement came in a brief filed with the U.S. Court of Appeals for the District of Columbia and is the second formal objection to the Obama administration’s latest accommodation process filed by religiously affiliated nonprofits since the administration announced the change in August.

Another religiously affiliated nonprofit, Little Sisters of the Poor, told the U.S. Tenth Circuit Court of Appeals this month that it, too, was pressing ahead with its claim and notifying the federal government that it was seeking an exemption from the contraception coverage requirement. Lawyers argued that the requirement unduly burdened the group’s religious rights.

In this latest filing, Priests for Life argued that it violates its religious rights to notify the Obama administration that it objects to providing contraception coverage because the act of doing so “impermissibly facilitates delivery of the objectionable coverage” and forces it to maintain a relationship with a company that will provide contraceptive coverage for the beneficiaries enrolled in their health plans.

In other words, the nonprofit objects to any federal government requirement that results in its employees obtaining contraception coverage.

The Obama administration responded telling the court in its brief, also filed Tuesday, that, “[I]t is one thing for plaintiffs to decline to provide coverage themselves. It is quite another to insist that they have a right to veto federal regulations that impose duties on other persons.”

Among the open questions in the nonprofit challenges to the ACA’s religious accommodation is the role “church plans” play in the dispute. Like Little Sisters of the Poor, Priests for Life has a “church plan” that, generally speaking, is not subject to the same statutes and regulations as other health insurance plans.

That would mean that those plans do not have to provide contraception coverage for their employees and that nonprofits like the Little Sisters and Priests for Life would face no economic consequences for failing to comply with the law.

But according to Priests for Life, the fact that some of these plans are “church plans” is irrelevant because “church plan” insurance administrators have the discretion to provide separate payment and coverage for contraception for those employees who want it.

The nonprofit argues that so long as nonprofits are required to maintain a relationship with an insurance company that can provide, even indirectly through reimbursements, contraception coverage, it will be complicit in the immoral conduct of facilitating access to birth control.

The solution, Priests for Life argues, is to have the government provide contraception coverage directly to those who need it, either in the form of tax credits or reimbursements for purchased contraceptive services, expanding eligibility for already existing federal programs that provide free contraception, or providing incentives for pharmaceutical companies that manufacture contraceptives to provide their products for free.

The Obama administration, however, disagrees, stating that “RFRA [the Religious Freedom Restoration Act] does not require the government to create entirely new programs to accommodate religious objections.”

The administration’s brief continued: “An employer with a religious objection to paying the minimum wage to female employees, for example, cannot simply demand that the government make up the difference with tax credits or direct provision of financial aid.”

The Obama administration also claims that Priests for Life and other groups challenging the accommodation process are at odds with the history of religious objections, which typically allows religious objectors to opt out and others to then fill their shoes. “On plaintiffs’ reasoning, a conscientious objector could object not only to his own military service, but also to opting out, on the theory that his opt out would ‘trigger’ the drafting of a replacement who was not a conscientious objector,” the administration noted.

Priests for Life’s case is one of more than 40 cases filed by religiously affiliated nonprofits challenging the birth control benefit accommodation process still pending in the federal courts.