First, the name had to go.

There could be no more talk, transit advocates reasoned, of “congestion pricing,” a phrase Mayor Michael R. Bloomberg often used before his sweeping plan to overhaul New York City’s bridge tolling system was vanquished in 2008, and treated as political arsenic ever since.

Then, with a clean slate, supporters could move on to the hard part: sculpting a proposal that might succeed where the mayor failed.

And so, more than five years after Mr. Bloomberg’s plan died in Albany, a cadre of the city’s transit minds has primed a successor, fine-tuning a pricing model that might be more palatable to residents outside Manhattan, meeting quietly with former opponents and preparing to take its case early next year to a public that has grown accustomed to free, if traffic-choked, rides over the East River.

Political obstacles abound, including securing the support of the State Legislature. But in what the plan’s supporters have billed as the most significant change of heart so far, Councilman Mark Weprin, an outspoken critic of the old proposal, said in an interview last week that he was receptive to this reimagined version.