Sen. Thom Tillis (R-N.C.) sent a letter to his GOP colleagues Sunday targeting proposed rule changes from the right flank of Senate Republicans — and offering some alternative ideas of his own.

The North Carolina senator has been vocally railing against Senate conservatives’ proposals — namely one that would impose a six-year term limit on the next Senate GOP leader, which he argues would weaken the position. Outgoing Senate Minority Leader Mitch McConnell has echoed those concerns. In the letter, Tillis notes that the Senate Democrats’ leader has no term limits, nor does either party in the House.

“Mitch [McConnell] has been elected 9 times and 8 of those were unopposed,” Tillis wrote in the letter. “Nothing has prevented any member from mounting a challenge in the past. Having terms limits on the leader could make the political side of the job more difficult.”

But Tillis goes on to point out areas he suggests the conference could improve. He specifically compared Senate Republican conference rules to Senate Democrats’ caucus rules — and outlined differences that he thinks give Senate Democratic leaders a leg up. He said he is not outright “advocating” for any rules changes, but instead “providing food for thought on how we could address some of the frustrations of our members.”

It’s the latest evidence of Senate Republicans’ rift over the future of their party conference, where the race to succeed McConnell is ramping up. Sens. John Cornyn (R-Texas), Rick Scott (R-Fla.) and John Thune (R-S.D.) have all entered the race, and questions over new rules they’d support are becoming centerpoints of their bids.

Among those differences in party rules, Tillis noted the Senate Democratic leader gets to appoint the chair of the caucus’ campaign arm, a selection that is “ratified by the conference.” He said allowing the Republican leader, who currently does not appoint the Republican campaign-arm chair, to do the same could prevent intraparty friction.

“Having the leader nominate the [National Republican Senatorial Committee] chair subject to conference ratification could make it more likely the NRSC chair will be in alignment with the priorities of the Republican leader and reduce the risk of conflicts in messaging and priorities,” Tillis wrote.

The senator also pointed out differences in the committee-assignments process between Republicans and Democrats. Currently, the Democratic leader is in charge of filling all open committee spots, while the Republican leader has more limited power over such assignments.

Tillis wrote that expanding the GOP leader’s authority over committee assignments to match Democrats’ “could empower the leader to position members on committees most likely to carry the agenda of the majority of the conference forward.”

The senator identified a number of other proposals, including tweaks to the amendments process and rules for blocking action on the floor. He also proposed new conditions that would compel the leader to close a vote that’s gone past its allotted time if just one member has not voted and that member’s vote would not change the outcome, among other parameters. That would speed up votes on the Senate floor, which regularly go on for an hour or more as members trot in and out.

“These could be adopted by a vote of the conference and would be non-binding to members but would serve more as public guiding principles,” Tillis wrote.

There’s a long time between now and the leadership elections, when the bulk of these ideas within the conference will be put on the hot spot. And other ideas for rules changes are likely to come out as GOP senators decide which leadership candidates they’ll throw their weight behind.

But Tillis said he was just getting started.

“This is by no means an exhaustive list. I share it as a starting point for a discussion of the pros and cons of any changes as we make our first transition in conference leadership in 18 years,” Tillis added. “Looking forward, I believe a thorough discussion of these, and other ideas would be a good use of our time.”