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Although Mr. Monaghan could be the best-known figure in the dispute — he used to own the Detroit Tigers — he is “actually pretty low-profile” and not speaking directly to the media about the cases, Ms. Mersino said.

At Ave Maria, Mr. Monaghan sits on the board of trustees and may assist fundraising, but is not involved in the day-to-day operations of the school, said university President H. James Towey.

However, Mr. Monaghan offered a founding vision for the institution and donated $250 million to establish its campus about 30 miles from Naples, Fla., according to the university’s website.

Like many other institutions, the university is pressing forward with its legal claims after rejecting the Obama administration’s solution to the contraception question.

“The fact remains, they are trying to make us complicit,” Mr. Towey said.

On the corporate side, Mr. Monaghan is the owner and sole shareholder of Domino's Farms, a 937,203-square foot office park in suburban Ann Arbor, Mich., that includes a Catholic bookstore and chapel that holds Mass four times per day, Ms. Mersino said. The corporation does not offer contraceptive coverage to its 45 full-time and 44 part-time employees, nor does it plan to, its lawsuit says.

According to the lawsuit, the Obama administration, “in an unprecedented despoiling of religious rights, forces religious employers and individuals, who believe that funding and providing for contraception, sterilization, abortion, and abortifacients is wrong, to participate in acts that violate their beliefs and their conscience — and are forced out of the health insurance market in its entirety in order to comply with their religious beliefs.”

Michigan Attorney General Bill Schuette has filed legal briefs in support of Mr. Monaghan’s company and two other plaintiffs from his state.

“Religious liberty,” he wrote, “cannot be confined to the sanctuary and sacristy.”