Republican presidential campaigns agreed Sunday to side-step party leaders and try to negotiate directly with television networks over the ground rules for the remaining debates following controversy over last week's CNBC event.

At least one campaign refused to rule out holding debates that are unsanctioned by the Republican National Committee, with Ben Carson campaign manager Barry Bennett saying that he didn't think it would be hard to buy television airtime for such an event.

Representatives from more than a dozen campaigns met behind closed doors for nearly two hours Sunday night in suburban Washington, a meeting that was not expected to yield many results given the competing interests of several candidates. Yet they emerged having agreed to several changes to be outlined in a letter to debate hosts in the coming days.

Bennett said the demanded changes include largely bypassing the RNC in coordinating with network hosts, mandatory opening and closing statements, an equal number of questions for the candidates, and pre-approval of on-screen graphics.

"The amazing part for me was how friendly the meeting was," Bennett said, noting the private gathering was held in a private room marked "family meeting." "Everybody was cordial. We all agreed we need to have these meetings more regularly."

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The GOP's most recent debate in Boulder, Colo., on Wednesday night, drew harsh criticism from the campaigns and GOP officials alike. Afterward, some candidates complained that the questions were not substantive enough; others wanted more air time or the chance to deliver opening and closing statements.

GOP chairman Reince Priebus decided to suspend a partnership with NBC News and its properties on a debate set for February, but that wasn't enough to satisfy the frustrated campaigns.

"We need to mature in the way that we do these debates if they're going to be useful to the American people," Carson told ABC's "This Week."

While the campaigns agreed to the changes in principle Sunday night, the media companies that host the debates are under no obligation to adopt them. Bennett suggested that campaigns could boycott debates to get their way.

"The only leverage we have is to not come," he said.

The pushback comes despite a high-profile effort by the Republican National Committee to improve the debate process going into the 2016 election season. The party said the 2012 debate schedule promoted too much fighting among candidates, so for 2016, the RNC dramatically reduced the number of debates for this election and played a leading role in coordinating network hosts and even moderators, in some cases.

Three debates remain before the first nomination contest, the Iowa caucuses on Feb. 1; the next one is scheduled for Nov. 10 in Milwaukee. The RNC has sanctioned five debates after the caucuses.

"What it really comes down to is the candidates want to have more control of the ability to negotiate with the networks," Donald Trump campaign manager Corey Lewandowski said after the meeting.

While organizers of the meeting were not including the RNC, the party has been in regular communication with campaigns about their concerns.

Shortly before the meeting, the RNC appointed Sean Cairncross, the committee's chief operating officer, to take the lead in negotiating with the networks. It's unclear, however, what role he'll play should the campaigns get their way.

"This is the first step in the process of understanding what the candidates want, and then we need to have a more specific conversation about NBC," RNC chief strategist Sean Spicer said Sunday ahead of the meeting. "We need to start a process. Tonight's the first step."

Some candidates are trying to use the debate discord to their advantage -- none more than Texas Sen. Ted Cruz.

Campaigning in Iowa this weekend, he slammed the CNBC debate moderators for asking questions in a way that he said "illustrate why the American people don't trust the media." He was cheered after calling for future debates to be moderated by conservatives such as radio host Rush Limbaugh.

Fox News' Jason Donner and Jenny Buchholz and The Associated Press contributed to this report.