No board of trustees likes to see internal disputes splashed on the front page of the newspaper, but it’s happened again.

This time it’s not the University of Massachusetts or even long-suffering Suffolk University, but the board of Boston College High School. The issue, as my colleague Jamie Vaznis reported on Saturday, is whether the elite all-boys school should — gasp! — start admitting girls.

A recent letter sent out by chairman John McQuillan seemed to leave open that possibility, and the notion is pitting board member against board member at the Jesuit Catholic school in Dorchester. Riled-up alumni, parents, students, and faculty are split too. Some alums have vowed to fight going coed, even threatening to stop donations. I wouldn’t be surprised if someone filed a lawsuit.

Emotions and tensions have been bottled up for so long that it is hard for anyone involved to think clearly. The factions no longer can agree on basic facts, such as whether the 154-year-old institution even has a problem. Try to make sense out of this: Applications are down 40 percent since 2008, but enrollment, by some accounts, is better than expected, with close to 1,600 students plus a waiting list.

After speaking to both sides, this much I am sure of: It’s time for an intervention before a civil war breaks out. Get it all out now. It would be a good thing.

I immediately thought of two people who could serve as mediators: Fidelity honcho Peter Lynch and advertising legend Jack Connors.

Lynch, after making a fortune as a star money manager, has devoted much of the past three decades to strengthening Catholic schools and has given more than $100 million to support everything from scholarships to teacher training.

Then a decade ago, Connors launched the Campaign for Catholic Schools, raising about $80 million to rebuild schools in the inner city and offer scholarships.

I couldn’t get Lynch to wade into the controversy swirling BC High, but Connors was not shy about dispensing advice.

“Boston College High School has played a very important role in the lives of many in this city,’’ Connors told me. “I’m hoping that they will bring in some serious minds both inside and outside to focus on their challenges — not just whether they go coed or not, but where they belong in the galaxy of quality preparatory education in the Greater Boston area.’’

The other big player who can offer guidance is Cardinal Sean O’Malley himself. Here’s why: If BC High goes coed, it will no doubt have an impact on other Catholic schools, namely all-girls institutions such as Fontbonne Academy in Milton and Notre Dame Academy in Hingham.

These schools might see their enrollment drop if some girls choose to go to BC High, which raises this question: Does it make sense to strengthen one parochial school if it means weakening another?

It’s a precarious time for both private and parochial schools in Massachusetts, where enrollment has dropped more than 20 percent over the past decade. Blame a combination of factors: the rise of charter schools, fewer school-age children, the squeezing of the middle class that is making private school out of reach.

BC High operates as an independent Catholic school, but still works with the Archdiocese of Boston, which oversees how the school teaches the faith. O’Malley has made Catholic school education a priority, and while enrollment at Boston-area parochial schools is down to about 37,500 students, the archdiocese still runs the second-largest educational system in Massachusetts after the city of Boston.

“We’re here to help them make the best possible decision. At the end, it’s BC High’s decision,’’ said Kathy Mears, the archdiocese’s superintendent of Catholic schools. “I know that they want to work with us. They don’t want to do harm to Catholic education in general.’’

The good news in all of this is that BC High is not facing an imminent financial crisis.

BC High attracts enough students to fill all of its seats and rests comfortably on a $70 million endowment.

What the board is attempting to do is talk about the future. That’s always tough when radical change is on the table. With some outside help, the board should get a fresh start on those discussions. It can’t avoid difficult conversations forever.

Shirley Leung is a Globe columnist. She can be reached at shirley.leung@globe.com. Follow her on Twitter @leung.