The first recent wave of legislation tightening voting laws came in 2021, when Donald J. Trump’s false claims of voter fraud spurred Republican lawmakers to act over loud objections from Democrats. Two years later, a second wave is steadily moving ahead, but largely under the radar.

Propelled by a new coalition of Trump allies, Republican-led legislatures have continued to pass significant restrictions on access to the ballot, including new limits to voting by mail in Ohio, a ban on ballot drop boxes in Arkansas and the shortening of early voting windows in Wyoming.

Behind the efforts is a network of billionaire-backed advocacy groups that has formed a new hub of election advocacy within the Republican Party, rallying state activists, drafting model legislation and setting priorities.

The groups have largely dropped the push for expansive laws, shifting instead to a strategy one leader describes as “radical incrementalism” — a step-by-step approach intended to be more politically palatable than the broad legislation that provoked widespread protest in 2021.

“They haven’t stopped trying to change how our elections are run. They’re just doing it out of the spotlight,” said Joanna Lydgate, the chief executive of States United, a nonpartisan election group. Some of the policies being promoted today will be law in time for next year’s presidential election, she added, “and American voters will feel the impact.”

Republicans have long said their goal is “election integrity,” but a spate of recent proposals suggests clear, and sometimes strikingly specific, political aims. National Republicans recently sought to change the rules for a single race in Montana — for the U.S. Senate — to tilt the scales toward the Republican candidate. In Ohio, Republican state lawmakers are seeking to make it harder to pass a ballot initiative, just as a coalition of abortion rights groups is collecting signatures to put a constitutional amendment on the ballot.

On a recent conference call with activists in Michigan, Cleta Mitchell, one of the chief architects of the new coalition, blamed “electoral systems” for the party’s losses in midterm elections, and not, as pundits have said, abortion messaging or poor candidates, according to a recording obtained by The New York Times.

“I think you have got to figure out what we have to do, where to fix the system that gives a Republican candidate a potential chance to win,” she said.

Ms. Mitchell declined to comment.

Incrementalism at Work

With some legislatures still in session, the full picture of new election laws is still coming into view. But this account of the state of the Republican campaign is based on documents, recordings and meeting minutes provided by Documented, a liberal investigative group, as well as on interviews and data analysis.

So far this year, 18 bills in 10 states have been signed into law that will add new restrictions to voting or election administration, according to an analysis of data maintained by the Voting Rights Lab. In 2021, the tally was 34 laws in 19 states.

For their part, Democrats have moved in the other direction — pushing to expand ballot access through more mail voting, adding new forms of acceptable identification to vote and expanding early voting. This year, 23 laws in 17 states and Washington, D.C., have been signed into law that will expand access to voting, according to the Voting Rights Lab.

The right’s shift to smaller steps is clear in Georgia and Florida, two battleground states that passed broad new laws a couple of years ago. This year, Georgia Republicans focused narrowly on banning outside funding for election offices. Florida passed a law that, among other provisions, puts new restrictions on voter registration groups.

While the downshift in ambitions is strategic, signs also suggest that Republicans have become wary of some types of restrictions. Party leaders have increasingly warned that its opposition to mail and early voting is discouraging Republican voters from casting ballots and costing the party races. Even Mr. Trump has been urging voters to cast ballots by mail, although he still suggests falsely that the system is rigged to favor Democrats.

In Idaho and South Dakota this year, Republicans joined with Democrats to vote down bills that would have effectively ended no-excuse absentee voting.

Familiar Forces Team Up

Ms. Mitchell, who played a central role in Mr. Trump’s effort to overturn the 2020 election, has become a leading force in the right-wing coalition.

Last year, her Election Integrity Network corralled thousands of activists to act as poll watchers and monitors in midterm elections. Now, Ms. Mitchell is working to turn those people into an enduring base of activists lobbying state lawmakers.

Ms. Mitchell’s network convenes regular meetings of lawyers, policy advocates, political operatives and state-level activists, some of whom promote the most far-fetched theories about hacked voting machines.

The coalition draws from a list of well-funded advocacy groups: the Honest Elections Project, which is backed by the 85 Fund, a nonprofit affiliated with the conservative activist Leonard Leo; the Election Transparency Initiative, a project tied to Richard Uihlein, a shipping supply magnate and Republican megadonor; and the Foundation for Government Accountability, which has received funding from both the 85 Fund and Mr. Uihlein’s foundation.

“The conservative side of the spectrum is largely playing catch up to the left, which has had an extremely well-organized, well-funded effort to push their progressive voting policies,” said Jason Snead, the executive director of the Honest Elections Project.

Ms. Mitchell’s priorities for the group include a mix of longtime proposals, such as ending same-day voter registration, and more recent fixations, like shortening early voting and prohibiting election offices from accepting private donations, known in some circles as Zuckerbucks, after the grants a nonprofit backed by Mark Zuckerberg gave to local election offices in 2020.

Some proposals buy into election conspiracy theories, such as pressing state election officials to withdraw from a once-obscure multistate database of voter roll information.

The database, known as ERIC, was long considered an important security tool and enjoyed widespread bipartisan support. But after theories spread claiming the system was part of a liberal plot to steal elections, activists in Ms. Mitchell’s network and others lobbied Republicans to turn against it.

Seven states have pulled out of the system.

Brendan Fischer, the deputy executive director of Documented, said such advocacy reflected the priorities of donors and leaders.

“These measures were not just a response to organic grass roots activism, but rather shaped and promoted by a cadre of dark money groups,” he said.

A New Player

Until recently, the Foundation for Government Accountability was best known as a Florida-based think tank that focused nearly all of its lobbying on seeking to dismantle government assistance programs like Medicaid, food stamps and other welfare initiatives.

But in early 2021, the group added election issues to its portfolio. A few months later, when Republican secretaries of state gathered at the Conrad hotel in Washington, D.C., for their annual conference, the foundation was the only outside organization with a speaking slot at every panel.

By 2022, the group’s fingerprints were on new voting legislation in Missouri, where its policy advisers assisted in crafting a voting bill that created strict new photo identification requirements, banned drop boxes and outside funding of elections and limited third parties from engaging in voter registration.

(The bill also added two weeks of early voting, but, in a provision apparently intended to discourage a legal challenge, those weeks would be revoked if a court struck down the new voter I.D. requirements.)

Jay Ashcroft, the Republican secretary of state of Missouri, said he had worked with the foundation on ideas and asked for help in creating legislative language. But when it came time to draft the bill, Mr. Ashcroft added, “F.G.A. wasn’t there. It was senators, it was representatives.”

By 2023, the group did explicitly write language. In Arkansas, for example, the Legislature passed a bill, and in April the governor signed it into law, establishing new rules for poll watchers. The legislation’s language was nearly identical to model legislation drafted by the foundation months earlier.

The group says its success in those states has been replicated across the country. In its 2022 annual report, it claims to have been involved in passing 70 “election integrity policy wins” across 19 states in 2022. That tally represents the success of “radical incrementalism” over “seismic shifts,” Tarren Bragdon, the foundation’s chief executive, said in a statement.

“Our view is it’s better to understand what is possible and pursue reforms that can get across the finish line with broad buy-in from voters and legislators,” he said.

Seizing on a New Issue

Another measure of the network’s influence is the rising opposition to ranked-choice voting, which allows voters to pick more than one candidate. Advocates for the system believe it gives voters more options and discourages political polarization.

But when reliably Republican Alaska was poised to elect its first Democratic member of Congress in nearly 50 years through ranked-choice voting, the network of think tanks and organizations on the right sought to turn lawmakers against the process.

The Foundation for Government Accountability and the Honest Elections Project each published reports criticizing ranked-choice voting as confusing and undermining voter confidence. The Honest Elections Project began a “Stop RCV” coalition.

In a January meeting of Ms. Mitchell’s legislative working group, Lynn Taylor, the president of the Virginia Institute for Public Policy, told activists in states across the country to connect with the foundation for model legislation that would ban ranked-choice voting, according to notes from the meeting.

In March, advocates with Opportunity Solutions Project, the nonprofit arm of the foundation, testified in favor of ranked-choice voting bans in Texas, South Dakota and Idaho.

Their coordinated efforts appear to have worked. At the end of 2022, only one state — Tennessee — had introduced legislation to ban ranked-choice voting.

Now, roughly four months into 2023, Republicans have introduced bans in six states. Montana, Idaho and South Dakota have each signed one into law.