The Trump administration has made clear of late that the end of the mortgage finance conservatorships could be near. As Mark Calabria, director of the Federal Housing Finance Agency, recently put it: “The status quo is over.”

But exactly what an overhauled market would look like is an open question. As the administration gets into the details of an eventual plan, they’ll need to navigate a number of sticky questions about how to get the government-sponsored enterprises out of federal control — including some that will bump up against other major banking debates.

One of the bigger ones is whether the GSEs should be considered systemically important. Although this is a topic that has largely flown under the radar up to now, it may take on new significance under a Trump-guided FHFA.

“All large, systemically important financial institutions should be well capitalized,” Calabria said at a housing event earlier this month, in speaking about his plans for Fannie and Freddie.

He elaborated a few days later, when questioned about whether there’s a role for the Financial Stability Oversight Council when it comes to the GSEs. (The FHFA director is a voting member on the council.)

“I certainly think it’s appropriate for FSOC to deliberate on whether Fannie and Freddie should be designated,” he said in an interview. “They’re large, important institutions that we’ve rescued once already, so I think that that’s a process that should happen.”

Long popular in some conservative circles, it’s an idea that appears to be gaining steam. Robert Kaplan, president and CEO of the Federal Reserve Bank of Dallas, recently indicated that he wants to see more stress testing of nonbanks, including Fannie Mae and Freddie Mac.

“We’ve been very well served in the banking regulation sector to do severe stress tests and very tough capital requirements,” Kaplan said at a journalism conference last week. “I would feel better if we also were applying vigorous standards and tests to nonbanks.”

Asked if that included Fannie and Freddie, Kaplan responded, “Yes is the answer.”

But one big problem with designating Fannie and Freddie becomes apparent when you look at the Trump administration’s changes to the SIFI designation process up to this point. In March, the FSOC proposed revising its process for labeling individual institutions as systemically important, emphasizing instead an activities-based approach to risk monitoring.

That significantly lowers the risk that the GSEs could be designated — a process that would subject them to greater oversight by the Federal Reserve — although it doesn’t necessarily eliminate it altogether.

“If you think about the risk of the activity, guaranteeing half the mortgage market, which is their whole business and political purpose, then I think it leads you very rapidly to designating them as institutions,” said Alex J. Pollock, a distinguished senior fellow at the R Street Institute.

Such an examination could expose some important tensions, especially given the administration’s move away from designations more broadly.

“A designation is not a punitive device that should be wielded against one’s foes,” said Gregg Gelzinis, an economic policy analyst at the Center for American Progress. “What are the tools and authorities that Calabria currently lacks to ensure the safety and stability of these firms?”

Under the Dodd-Frank Act, firms that are labeled as SIFIs come under additional scrutiny from the Federal Reserve.

Moreover, if Congress fails to act on mortgage finance reform (which seems more than likely at this stage), and Calabria opts to move forward unilaterally, he’ll need to strike a crucial balance between establishing that the GSEs can attract enough private capital, while also ensuring they face strict standards. Calabria said in a speech on Monday that Fannie and Freddie’s ability to emerge from conservatorship will be “driven, first and foremost, by their ability to raise capital.”

“The disconnect here is conservatives want tough, banklike capital — but in the end, you’re going to have to allow these companies to be profitable enough to recapitalize,” said Charles Gabriel, president of advisory Capital Alpha Partners.

Perhaps most critically, it won’t take a formal designation for a SIFI discussion to influence the broader debate. Simply raising the issue, or having the FSOC conduct a preliminary review, could ultimately influence reform efforts.

“Just by saying he wants to elevate mortgage securitization as a systemically worrisome activity, what that could do is arm him to push for slightly tougher capital standards,” Gabriel added.

As discussions about housing finance heat up, the fight over SIFIs could evolve with it.

Kate Berry contributed reporting. Bankshot is American Banker’s column for real-time analysis of today's news.