There are still a few Republicans in Congress who are interested in addressing the status of the 690,000 or so young unauthorized immigrants facing the loss of their temporary deportation protections under the Deferred Action for Childhood Arrivals (DACA) program. And they’re beginning to turn up the pressure on House Republican leadership to bring a bill to the floor.

Or rather, four bills.

Moderate Republican Reps. Jeff Denham (R-CA) and Will Hurd (R-TX), together with members of the Congressional Hispanic Caucus, announced a resolution Tuesday that escalates — slightly — a DACA fight that looked dead for the year. It’s probably not a coincidence that Hurd and Denham are two of the House members most at risk of losing their seats to Democrats in November.

Their proposal: to use an obscure House rule called the “queen of the hill” to hold votes on four different immigration bills. Two of the bills they have in mind would give permanent legal status to DACA recipients; a third would be the conservative bill written by Rep. Bob Goodlatte (R-VA) that the conservative House Freedom Caucus has been pushing, which would grant temporary status to DACA recipients in exchange for deep cuts to legal immigration and beefed-up interior enforcement; and the fourth bill would be up to Paul Ryan to decide.

Which bills come to the House floor is pretty much up to the speaker, and it’s not clear that Paul Ryan (who has been squeamish, as speaker, on immigration) is on board. But here’s where it gets interesting. The backers of the “queen of the hill” plan say they have 240 members in support of their procedural gambit — enough, if they wanted, to override Ryan and force the votes to the floor. The question is just how far Denham and company are willing to go.

The “queen of the hill” rule: the bill that gets the most votes wins

When the Trump administration announced in September that it was winding down the DACA program, members of Congress from both parties leaped to promise that they’d pass a bill in the next six months to prevent the immigrants protected by the program from losing their work permits and deportation protections en masse starting in early March.

But after it became clear that President Trump and the White House weren’t committed enough to a DACA deal to make any actual compromises — and after federal judges stepped in to partially reopen the DACA program by allowing current recipients to apply for two-year extensions while lawsuits over the program’s future make their way through the courts — most Republicans lost appetite.

The Senate held a cursory debate on immigration in February but couldn’t get 60 votes to break a filibuster on any bill (though the bill Trump supported did get 60 “no” votes). The House never moved a bill at all.

House inaction frustrated both Democrats and moderate Republicans — who were convinced the House had the votes to pass a bill to legalize DACA recipients — and Freedom Caucus members who backed the Goodlatte bill. (Ryan reportedly promised the Freedom Caucus he would bring Goodlatte’s bill to the floor but hasn’t done it yet, raising questions about whether he’s struggling to find the votes for it or just dragging his feet.)

The “queen of the hill” plan solves these problems. It would bring four bills, in a series, to the House floor for a vote, and whichever one got the biggest vote margin in favor would pass:

The Goodlatte bill (temporary status for DACA recipients plus stepped-up enforcement and legal immigration restrictions)

The DREAM Act (a path to citizenship for DACA recipients and other DREAMers, with no enforcement trade-offs)

The USA Act sponsored by Hurd and Rep. Pete Aguilar (D-CA) (quicker legalization for DREAMers with limits on sponsorship of parents once they become citizens, with some border provisions but no money for a wall)

A fourth bill, up to Paul Ryan to decide

These bills are mutually exclusive. But because of the “queen of the hill” rule, members who supported more than one would be able to vote for more than one — because even if two bills got 218 or more votes, only one of them would actually be passed under the rule.

Normally, it’s up to the House Rules Committee (which attaches procedural rules to every bill that comes normally to the House floor) to decide when to use the “queen of the hill” rule. But Denham and company have proposed a resolution to use the rule on the four immigration bills — so if 218 members of the House voted in favor of the resolution, it would trigger the “queen of the hill” quartet. And they claim they have 218 votes, and then some.

Are moderate Republicans willing to force Paul Ryan’s hand on DACA?

It’s hard to get 240 members of the House to agree on anything, so if the Denham-CHC group has its math right, they’ve already accomplished something impressive. But just getting 240 people to say the “queen of the hill” plan is a good idea doesn’t bring it any closer to the House floor, unless it suddenly inspires Paul Ryan to have a change of heart.

Members whose priorities are stuck in limbo often threaten to start a “discharge petition” to bypass the speaker and bring a bill to the floor. But few discharge petitions can get the 218 signatures needed. If all 240 members who support the “queen of the hill” plan put their signatures where their mouths are, it actually would. Which makes it all the weirder that they’re not planning to start one — at least not yet.

Hurd said that they “reserve the right” to use procedural tools like a discharge petition if they don’t get their way. But they’re hoping they won’t have to. Denham said Wednesday that “when you can show the overwhelming majority of the House that is supportive of this, you shouldn’t need a discharge petition” — which is a little puzzling because those are the only times a discharge petition can actually be used.

Denham, Hurd, and a handful of other Republicans are in a tricky position in 2018. They’re moderates in purple (and diversifying) districts. Their ability to hang on to their seats depends on the ability to both distance themselves from Trump and make voters feel that they are getting something done that’s worth keeping them in office. Supporting a policy like the legalization of DREAMers does the first — but supporting a proposal that isn’t going anywhere doesn’t help with the second.

The “queen of the hill” plan is a sign that some Republicans might be willing to pressure their own leadership to take some action on immigration. But it’s obviously not enough on its own, and it’s still an open question how far the Republican dissidents are willing to go.