CLEVELAND — The first presidential debate took place in Cleveland on Tuesday night, but it wasn’t the candidates’ policies that took center stage: Instead, viewers lamented the utter chaos and sheer amount of interruptions from both President Donald Trump and Democratic candidate Joe Biden during their 90-minute appearance. 

The nonpartisan Commission on Presidential Debates, the organization that hosts all presidential and vice presidential debates, also took notice of the night’s unconventional flow — and may implement changes to future debate structures to mitigate the problem. 

“The Commission on Presidential Debates sponsors televised debates for the benefit of the American electorate,” the company wrote in a statement on Wednesday. “Last night’s debate made clear that additional structure should be added to the format of the remaining debates to ensure a more orderly discussion of the issues. The CPD will be carefully considering the changes that it will adopt and will announce those measures shortly.” 

One of the changes reportedly being considered is the ability to cut off a candidate's microphone if they violate rules, according to CBS News, citing an informed source.

The organization also thanked debate moderator Chris Wallace for the “professionalism and skill he brought to last night’s debate,” adding that the commission “intends to ensure that additional tools to maintain order are in place for the remaining debates.”

Over the course of the night, Wallace repeatedly asked both candidates to stop interrupting each other, although his comments of “sir, I’m the moderator,” and “your time is up,” were most often directed at the president. 

At one point, Wallace told the president: “Frankly, you’ve been doing more interrupting” than Joe Biden.

Both candidates talked over one another when answering questions about everything from the coronavirus pandemic to the Supreme Court.

At one point, the former Vice President was apparently so fed up with interruptions from the president, Biden snapped at Trump, “Will you shut up, man?”

Some viewers wondered on social media why Wallace didn’t simply mute the mics of one person to allow the other to talk, but as neither Biden nor Trump’s campaign agreed to be muted ahead of time, Wallace’s hands were tied. 

“On social media, some viewers at home called for the president’s microphone to be shut off, but that was a power Mr. Wallace did not possess: Neither campaign would have agreed beforehand to such a mechanism,” the New York Times reported. 

Even if they had agreed to such a proposition, there’s no guarantee it would work — afterall, the Trump campaign agreed that each candidate would have a certain amount of time for uninterrupted comments, but as Wallace pointed out, the president did not comply with these rules during the debate.

The commission has not yet revealed what changes it will implement in future debates. 

But the announcement came as some media personalities and political experts declared that the first debate was such a poor showing that both upcoming presidential debates should be cancelled.

Dr. Larry Sabato, Director of the University of Virginia’s Center for Politics, declared Tuesday’s event as “the most incoherent debate I have ever watched” in an interview with CBS on Wednesday. 

While Tuesday’s debate was in progress, Dr. Sabato tweeted that all remaining presidential debates this year should be cancelled. 

“I don't know that it's going to be possible to restructure this. How are the Trump people going to allow the rules to change?” Dr. Sabato told CBS when asked why he thought the debates should be cancelled instead of altered, adding: “I don't think the next two (debates), if they have them, will be as bad as the one last night.” 

TV hosts across multiple major networks also pondered aloud about the future of this year’s presidential debates. 

"It will certainly raise a lot of questions ... about the future of presidential debate between these two candidates,” CNN anchor Wolf Blitzer said during the network’s post-debate coverage. “I wouldn't be surprised, by the way,  if this is the last presidential debate between the president of the United States and the former vice president of the United States.” 

MSNBC’s “Morning Joe” co-host Joe Scarborough tweeted that the event was a “low point in American debate history,” adding: “There is no reason, not one, that Joe Biden should participate in another debate.” 

Even conservative pundit Laura Ingraham agreed following Tuesday’s event that “the traditional model for presidential debates doesn't work very well,” although she called for altering the format instead of eliminating future debates altogether. 

“What we need now is a model that gives the candidates more time to explain their views and to lay out for voters what's really at stake. Because like it or not, the voters have to choose -- not us in the media, but you," Ingraham said.

"Now, this isn't like 2000, when the stakes were just not not all that big. Losing this election will really hurt — and will hurt for a very long time. I think the more you let everyone have their say, even if they're angry and upset, the better off we'll all be,” she continued.

On the other hand, several prominent Fox News hosts and conservative political pundits praised the president’s appearance. 

“Trump's strategy tonight was executed brilliantly,” Fox News contributor Dan Bongino said on Tuesday night, calling the president an "apex predator," "the lion king," and "the shark in the ocean."

Biden’s campaign pushed back against suggestions to cancel upcoming debates. Biden’s running mate Kamala Harris joined CNN’s Jake Tapper following the debate, when the host asked Harris if she thinks the former vice president should consider cancelling the final two debates. 

“Joe Biden’s never going to refuse to talk to the American people,” Harris replied. “And have any opportunity that he can to speak directly to American families and speak about the issues, speak the truth, and address the facts of where we are now, but also address the hopes and dreams of the American families and where we could be and Joe’s got a plan for dealing with those hopes and aspirations as well.”

As for Trump, the president seemingly thought the debate went over quite well for his campaign. 

“I thought the debate last night was great, we've gotten tremendous reviews on it. We're hitting what people want, law and order, which Biden was unable to even talk about because they’d lose the radical left,” Trump told reporters on the White House lawn on Wednesday.

In fact, Biden did discuss law and order during Tuesday’s debate, at one point saying: “Yes, I’m in favor of law and order. Law and order with justice, where people get treated fairly.”

Later on, the president questioned on Twitter why he would approve a change to the debate rules when he so "easily won last time."

On a conference call with reporters, Trump’s reelection campaign indicated that Trump would attend the remaining debates regardless of whether the rules are changed.

“We’re ready to move on to the second and third debates,” said campaign communications strategist Jason Miller. “There shouldn’t be any changes. We don’t want any changes.”

The Associated Press contributed to this report.