“This is a historic moment,” said Elaine C. Kamarck, a senior fellow at the Brookings Institution and an expert on the presidential nomination system, who noted that the parties could choose two very different paths.

“One possibility is that the system moves even in a more public direction than it has,” Ms. Kamarck said. She suggested that the parties could open their primaries to even more voters in a way that reduces the influence of activists and leaders.

“The other end of the continuum is the possibility that parties begin to take back some of their prerogative to nominate their candidates,” she said.

“The question at this inflection point,” she said, “is which way does it go?”

The superdelegate system in the Democratic Party has become the subject of fervent criticism from Mr. Sanders and his supporters because of the outsize role it gives to members of the party elite in choosing the nominee. That would be one obvious target for reform, Democrats said.

But the changes being considered by Republicans have been more thoroughly discussed. And they include several proposals for reordering the political calendar, which has traditionally begun with Iowa as the first state to vote, followed by New Hampshire, South Carolina and, since 2008, Nevada.

In one possibility that members of the Republican National Committee have floated, the early voting states, also known as “carve-out states,” would retain their special status. But to bring more states into the process earlier, each would be paired with a nearby state that would vote on the same day. So Iowa would still hold the first contest in 2020, but on the same day as Minnesota. New Hampshire would vote next, but on the same day as Massachusetts. And the same-day pairings would change: In 2024, Iowa would be twinned with South Dakota, and New Hampshire with Maine.

“I think there will be a serious discussion about the carve-out states and how that process works,” said Henry Barbour, the national committeeman from Mississippi and a member of the convention Rules Committee.