The previous three mayors - William M. Breichner, Robert E. Bruchey II and Steven T. Sager - have agreed to be part of the panel, if it's created.
During an interview Wednesday afternoon, the current mayor, Richard F. Trump, questioned both the intent of the commission and the choices.
"Two of those people I beat in the election," Trump said. "One of 'em I beat twice. So, if he is suggesting that is a fair representation to sit down and review issues that are going on right now, I find that to be a very biased group of people.
"I don't think the community should be interested in changing the charter," Trump continued. "I think ... the council and the mayor need to work through these issues, which I don't think are big issues. I think they can be worked through easily."
Last week, all five council members sent Trump a letter putting him "on notice" for his "failure to follow basic rules of procedure, decorum and civility." The mayor and council have clashed at several meetings.
Metzner stressed Wednesday that his plan is not a reaction to the recent turmoil.
"It has absolutely nothing to do with this administration," he said.
Metzner said he can't imagine any major changes being made during the current administration.
The only specific example he would give for possible study was whether the mayor should need a majority of the vote to take office, giving him or her a mandate from the electorate.
In the May election, Trump received about 39 percent of the vote and Breichner received about 33 percent. Bruchey, a write-in candidate, received about 28 percent.
Metzner said he thought more about his idea recently when he studied the charter again, in the midst of the council's conflicts with Trump.
Metzner said he likes the symbolism of three mayors - one-time election rivals - working together, even if they favor more mayoral power.
The city's current system switched to what's known as a "weak mayor" in 1983, he said.
Metzner said his idea might come up again at a work session. Or, he might just ask at least two other council members to sign on and set up the panel.
During Tuesday's meeting, Councilwoman Kelly S. Cromer said she supports Metzner's proposal.
Breichner said there was a good balance between the council and mayor while he was in office, but added, "There are times when you feel helpless."
Sager said that before he served, the mayor's right to vote had been traded for the right to veto. He estimated that he exercised his veto power about two or three times during 12 years in office.
As mayor, though, with no right to vote, "you feel sort of all dressed up with no place to go ...," Sager said. "The public holds you accountable as if you have a vote."
Bruchey said he never felt the need for more power. The only thing that frustrated him, he said, was how slow government sometimes worked.
Sager was mayor from 1985-97, when he lost to Bruchey.
Bruchey served one term, losing to Breichner in 2001.
Trump beat Bruchey in this year's Republican primary, then defeated Breichner and Bruchey in the general election.