One scenario for the Big East’s football future is for the conference to add Air Force and Navy, above, along with Army and possibly three other schools for football. (Jonathan Newton/WASHINGTON POST)

With TCU formally jilting the Big East on Monday, conference officials announced they’re considering doubling their football-playing ranks from six — after Syracuse and Pittsburgh bolt for the ACC — to 12.

One scenario for beefing up Big East football would make a powerful statement in terms of prestige and patriotism, with all three service academies — Air Force, Army and Navy — targeted for inclusion.

It’s unclear if the academies have discussed joining the Big East en masse or whether a refusal by one would scuttle interest by the other two.

But Navy and Air Force have discussed football-only membership with Big East officials, and Army is being courted.

“We certainly look at this as a very viable option for football only,” said Troy Garnhart, Air Force associate athletic director for communications, in a telephone interview Monday.

Air Force officials already have explored moving their other sports from the Mountain West to the Missouri Valley Conference. Over the weekend, Air Force Athletic Director Hans Mueh told the Denver Post that under his perfect scenario, Army and Navy would join Air Force in the Big East.

Navy Athletic Director Chet Gladchuk reiterated his concerns Monday about the Big East’s stability going forward, alluding to speculation that Louisville or West Virginia may depart next.

“My question still remains, as it has been since Syracuse and Pittsburgh left, what’s the status of the six that I call the anchor schools that are part of the Big East today?” Gladchuk said in a telephone interview. “Going to 12 is only half the equation. The other side of the equation is the importance [of] those six institutions, which I think are critical to the stature of the conference. Have they come to the conclusion yet that they’re all in? I haven’t heard that yet.”

Army, which competes as an independent, reportedly has reservations about the demands of competing in a conference after an unsatisfactory experience in Conference USA.

Gladchuk said that Navy, also an independent in football, was close to deciding on joining the Big East before Syracuse and Pittsburgh announced in September that they were leaving for the ACC.

“We’re not removed from this process at all; we’ve been very much involved, probably more so than anyone else, to be perfectly honest with you, outside the immediate membership,” Gladchuk said. “Meantime, we’re very careful in some of the ground rules that we felt were important. And one of the ground rules has to do with the commitment of the six foundation schools right now. It’s wonderful that they decided to go 12. Let’s start with the first six: Are they in?”

(As of 2014, the Big East’s remaining football schools are Cincinnati, Connecticut, Louisville, Rutgers, South Florida and West Virginia).

To that end, Big East officials continue debating the merits of raising their exit fee from $5 million to $10 million.

But no action was taken during a Monday morning conference call among the remaining 14 university chancellors and presidents.

With 12 football-playing members, the Big East could stage a conference championship football game, thus generating a new revenue stream.

Under that scenario, two of the six new members likely would be added in all sports.

Temple would be an attractive candidate. It has a storied men’s basketball program and a resurgent football squad.

Central Florida could be another.

That would leave one vacancy (assuming Louisville and West Virginia stay, and all three service academies join as football-only members), which could go to East Carolina. That would bring to seven the number of schools the Big East has plucked from Conference USA since 2005 (when Cincinnati, Louisville, South Florida, DePaul and Marquette were added).

It’s also possible the Big East could go with 10 football teams. (The NCAA requires conferences to have at least eight members.)

Air Force hardly fits the Big East’s traditional geographic niche.

But that’s part of the appeal for the Falcons, Mueh told the Denver Post, noting that the opportunity to compete in Big East would help with recruiting — for the Academy as a whole, as well as athletics.

The Big East would benefit in myriad ways if all three academies came on board.

For one, the academies would bring an audience without geographical boundaries.

The conference would also serve as home for the Commander-in-Chief’s Trophy, which since 1972 has been awarded to the victor of the annual football series among Army, Navy and Air Force.