Several members of the Board of Supervisors said that sinking more money into Muni and granting more authority to the agency which oversees it may not be the best fix for the ailing transit system.

A charter amendment from Board of Supervisors President Aaron Peskin is designed to improve Muni service and require the Municipal Transportation Agency to reduce carbon emissions.

The board’s Rules Committee will hold further discussions Tuesday, when the committee is expected to send it to the full board for a likely vote July 17. At least six board votes are needed to make it onto the November ballot.

The amendment wouldincrease MTA’s autonomy, such as granting sole power to set the dollar amount of parking fines, and funnel an additional 40 percent — for a total of 80 percent — of The City’s parking revenues to MTA.

Under the proposal, The City would hand an additional $26 million to Muni next fiscal year.