“Every two years I bring my progressive record to the people of the 16th District and ask them for their support,” Mr. Engel said in a statement. “As always, I will continue to do all I can as a member of Congress to earn their vote.”

The campaign arm for House Democrats, the Democratic Congressional Campaign Committee, has vowed to defend incumbents, brushing off the ire of liberal Democrats as it broke ties with pollsters and political consultants who work for primary challengers. And some strategists say that while warding off so many challengers may be costly, having them split the vote is ultimately beneficial for the incumbent.

“Once you have one primary challenger, you would like to have several more,” said Steve Israel, a retired congressman from New York who once led the Democratic campaign arm. “They dilute the base.”

Adam Green, co-founder of the Progressive Change Campaign Committee, said in an interview that his group had debated having progressive challengers pledge to leave a race if a front-runner was clearly established against the incumbent.

Aware of the influx of candidates, several liberal insurgent groups, like Democracy for America and Justice Democrats, are embarking on a more intentional process of endorsing candidates this election cycle. Mr. Bowman is the first New York candidate Justice Democrats has endorsed, and only the second candidate this year. (Last election, the group endorsed 78 candidates and recruited 12 to run for office.)

“We’re always going to take risks,” said Alexandra Rojas, the executive director of Justice Democrats. But, she added, “we’re going to be a lot more intentional about going into districts and then doing a handful of seats.”

About 70 House districts held by Democrats have at least one challenger filed with the Federal Election Commission, months before the primary elections. Many candidates, like Marie Newman, a contender against Representative Daniel Lipinski in Illinois’s Third Congressional District, are trying for a second time after narrowly losing their races in 2018.