Four years ago, left-leaning Democrats were struggling to coalesce behind a mayoral candidate to lead New York City. Their fissures helped a moderate Democrat, Eric Adams, win the primary and become mayor.

Now, as Mr. Adams seeks a second term under the cloud of a five-count federal indictment, the city’s progressive leaders are hoping to do whatever it takes to install one of their own in City Hall — or, at the very least, make sure that Mr. Adams is defeated.

“The left was extremely disorganized and divided last time, and we want to make sure that we have a strategy to keep our side together,” said Ana María Archila, a co-director of the state’s Working Families Party. “We must transfer the mayor’s office from someone who has been working for the rich and his friends to someone who will work on behalf of working families.”

The city’s relatively new ranked-choice voting system, which allows voters to rank up to five candidates in order of preference, could lead to interesting alliances and novel strategies from major interest groups.

The Working Families Party will back a slate of candidates in its preferred order, and will ask voters to leave Mr. Adams — and perhaps former Gov. Andrew M. Cuomo, should he enter the race — off their ballots entirely. Other progressive groups and unions will make their own endorsements in the coming months.

The hope on the left is that voters will express their anger over President Trump’s victory in November by flocking to the polls, and that they will choose a candidate who wants to stand up to Mr. Trump, not embrace him as Mr. Adams has recently done.