COATESVILLE, Pa.—Chrissy Houlahan nursed a chocolate milkshake at a diner here on her way to a gun-control event and pondered the changing political nature of this Philadelphia suburb, which has been represented in Congress by an uninterrupted chain of Republicans for more than 100 years.

“If you had told me 10 years ago, here in Chester County, that we were having a conversation about this issue, I would not have believed you,” said Ms. Houlahan, the Democratic candidate for Congress representing Chester County.

Nine of Pennsylvania’s 18 House seats could change parties this year, a concentration of competitive races like nowhere else in the country due to the combination of court-ordered redistricting and a broader realignment of suburban voters away from the Republican Party.

Of the 66 GOP-held House seats that the Cook Political Report rates as lean Republican, a tossup or likely or lean Democratic, 31 come from six states. Democrats could run the table in battlefield districts in just four states—Pennsylvania, California, Florida and New Jersey—and capture the net 23 seats they need to seize the House majority without taking a single district anywhere else.

In 2006, Democrats won a House majority with success in rural seats in places like Indiana and North Carolina. Republicans took control in 2010 by wiping out those gains and winning districts held by rural and moderate Democrats. Four Pennsylvania seats changed parties in both 2006 and 2010, making it one of the most politically volatile states in each of the last two wave elections.

This year the battlefield is in the nation’s suburbs, districts that have sent Republicans to Congress for generations but are filled with educated women—a demographic that polling shows has fled the GOP more than any other in the Trump era.

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“The political winds are blowing six swing seats our way,” said Rep. Mike Doyle, a Pittsburgh Democrat who is the dean of the Pennsylvania House delegation. “It would not surprise me if our state flips more seats than any state in the country.”

In Pennsylvania, Democrats are counting on gains in places like Chester County, the only county in the state that backed both Mitt Romney in 2012 and Hillary Clinton in 2016. The county hasn’t sent a Democrat to Congress since the 19th century, said Terry Madonna, a professor at nearby Franklin & Marshall College who is an expert on Pennsylvania politics.

“In suburban districts, independent voters and women are shifting away from the Republican Party at a pretty significant rate,” said Ken Spain, a former communications director for the House GOP’s campaign committee.

Former U.S. Rep. Gabrielle Giffords and her husband Mark Kelly, pictured at a March news conference on gun control, campaigned Friday for Ms. Houlahan. Photo: Alex Wong/Getty Images

The new political dynamic was evident Friday, when Ms. Houlahan appeared in Coatesville with former Arizona Rep. Gabrielle Giffords, who was shot in the head outside a supermarket in 2011, and her husband Mark Kelly, the former astronaut who now runs Giffords: Courage to Fight Gun Violence, the gun control organization named for his wife.

Mr. Kelly and Ms. Giffords are in the midst of a nationwide tour stumping for Democratic candidates who back proposals such as universal background checks for gun purchases.

On Friday, they appeared with Ms. Houlahan and Mikie Sherrill, the favorite to win one of four of New Jersey’s competitive House races.

Among those here to support Ms. Houlahan was Nicole Bowman, a marketing writer from nearby Reading, Pa. After the school shooting earlier this year in Parkland, Fla., Ms. Bowman, 37 years old, started a local chapter of Moms Demand Action, the gun-control group backed by former New York City Mayor Michael Bloomberg. More than 100 people attended the first meeting.

“For a while it was a helpless feeling here,” Ms. Bowman said. “Now we have overwhelming support.”

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Ms. Houlahan, who has raised $2.8 million, is a heavy favorite to win in November against Republican Greg McCauley, who has raised just $174,000. After the Pennsylvania Supreme Court installed a new congressional map in February, the incumbent, GOP Rep. Ryan Costello, opted not to seek re-election. The Cook Political Report rates the race likely Democratic.

“We go where the opportunities are,” Mr. Kelly said. “This message does play well in certain places and it’s starting to expand.”

He traveled the state Saturday to also hold an event with Democratic Rep. Conor Lamb, who in March shocked Republicans by winning a special election in a Pittsburgh-area district Mr. Trump carried by 20 percentage points. Redistricting placed him in a district with three-term GOP Rep. Keith Rothfus, in a race the Cook Political Report rates as lean Democratic.

Mr. Lamb attributed his success to a hunger from voters for Democrats to engage with them.

“We hadn’t fielded candidates to run,” Mr. Lamb said. “I think it’s more about the ground game and getting out there and meeting people.”

His GOP opponent, Mr. Rothfus, said his constituents are happy with the local economy and cast his race against Mr. Lamb as a battle for the future of the Trump presidency.

“This race is a kind of bellwether for the country,” he said. “If we have Democrats take over the House of Representatives, you’re looking at impeachment proceedings against the president.”

Neither Mr. Lamb nor the House Democratic leadership has endorsed impeaching Mr. Trump.

At Mr. Lamb’s event Saturday at a firehouse in Heidelberg, Pa., Ron Landay, an allergist from nearby Mount Lebanon, said he abandoned the GOP because it stopped nominating moderates. By 2016, he had a Hillary Clinton sign in his front yard.

“The Republican Party went too far right wing,” he said.

—Follow regular updates and insights from the campaign trail at WSJ.com/CampaignWire

Write to Reid J. Epstein at reid.epstein@wsj.com

Corrections & Amplifications

Democrats could capture the House majority by winning in battlefield districts in just four states: Pennsylvania, California, Florida and New Jersey. The headline on an earlier version of this article incorrectly implied Pennsylvania by itself could swing Congress. (Sept. 10, 2018)