It’s always been expensive to raise a child in New York City. Try having three.

The median rent for an apartment with three or more bedrooms in Manhattan is over $7,000. Inventory for large rental apartments is at a six-year low. Day care for three young children can run some families $50,000 or even $100,000 a year.

The ever-rising cost of having a large family in New York has fueled an exodus of parents with young children that has accelerated over the last few years, transforming the city’s demographics, culture and politics.

The number of New York households with three or more children has dropped by nearly 17 percent over the past decade, according to an analysis of census data by the Center for an Urban Future, a think tank. The number of one-child households grew slightly, while two-child households held steady during the same period, indicating that large families are driving the decline.

“If we can’t hold onto families, we are giving up New Yorkers who would otherwise anchor our neighborhoods, schools and our tax base,” said Eli Dvorkin, the center’s editorial and policy director, who noted that New York’s decline in families with young children was worse than in other big American cities. “That’s not sustainable.”

In interviews, middle-class New York City parents of three said they were confronting the limits of what the city could offer their families.

Stephanie Park, who had her third child a few days ago, thought her and her husband’s finance careers would allow them to buy a home. But the cost of renting a three-bedroom apartment in Park Slope, Brooklyn, close to some of the city’s best public elementary schools, has left the couple falling far short of their savings goals. They are delaying homeownership indefinitely.

“We’re in lucrative industries and make a good amount of money, but in New York City, it becomes apparent very quickly how short of a distance your dollar actually goes when you stack up all the costs,” said Ms. Park, 39. “There are all these things that seemed to be so much more attainable for our parents’ generation.”

Rachael Kaighin-Shields, a social worker living in Clinton Hill, Brooklyn, largely stopped working after she had her third child because her salary could not compete with the cost of child care. Ms. Kaighin-Shields, 46, relies on hand-me-downs for clothes and toys for her three children, and she rarely buys Christmas or birthday gifts or hires babysitters.

While other families in her neighborhood have lavish birthday parties and take their children on vacations overseas, Ms. Kaighin-Shields said, “we go to the playground for birthday parties, and we make the cake. I’m OK with that, but if I wasn’t, I’d be miserable.”

Kat Casey, a psychotherapist, uses the second floor of her family’s home in Astoria, Queens, as her clinical office during the week, and rents out the space on Airbnb on the weekends, which she says is necessary to keep the family afloat.

“It takes a master’s degree in communications and logistical management” to raise a big family here, Ms. Casey, 39, said. “You have to have a super power of executive function to do this without gobs of money to throw at the problem.”

The difficulty of raising children in New York has begun to reshape the city’s politics, as elected officials try to one-up each other as the most family-friendly candidates.

Mayor Eric Adams has said his administration is working to make the city “the best place to raise a family” in the country. Gov. Kathy Hochul has sought to expand access to child care while reminding New Yorkers that she is the state’s “first mom governor.”

Zohran Mamdani, the Democratic nominee for mayor, has promised to provide free universal child care for infants as young as 6 weeks, making it the center of his campaign to deliver what he calls “a city we can afford.” After losing the primary, former Gov. Andrew M. Cuomo, who is now running as an independent in the general election, released a new slate of affordability proposals.

The reality of having a large family in New York is colliding with the Trump administration’s recent push for Americans to have more children. Rachel Campos-Duffy, the wife of Transportation Secretary Sean Duffy, recently summed up the goal in a social media post: “Fall in love, get married, have more babies than you can afford. Save America.”

That’s a complicated proposition in New York City, where people with three children often can’t find space to comfortably live together.

The median asking rent for an apartment with three or more bedrooms citywide is $4,800, according to data from StreetEasy, up from $3,300 in 2019.

Many three-bedroom apartments are rented by young people who split the cost with roommates, making the market even more competitive for families. And once renters find a decent family-size apartment, they tend to stay, reducing turnover for new renters; 43 percent of units with three or more bedrooms have been occupied by the same tenants for more than 10 years, according to the Center for an Urban Future.

The situation is similarly bleak for families trying to buy. The median asking price for homes with three or more bedrooms is nearly $1.8 million citywide, compared with $1.35 million in 2019, according to the StreetEasy data. The median price for those homes in Manhattan is $4.15 million, down slightly from $4.4 million in 2019.

Part of the problem is that real estate developers and politicians are under pressure to promote the number of new units built each year. So developers often flood the market with studios and one-bedrooms, whereas larger apartments offer them lower value per square foot.

That helps explain why, out of the roughly 191,000 apartments built over the past decade that received any amount of city subsidy, only about 3 percent had three or more bedrooms.

The situation doesn’t have to be quite so dire, said Mr. Dvorkin.

New York’s leaders could push to develop more family-size units on city-owned property, he said. Politicians could incentivize developers by offering greater subsidies for affordable housing projects with significant numbers of large apartments.

And if New York created more affordable housing for seniors, the city could free up thousands of large apartments occupied by older New Yorkers, including in public housing, who no longer need so much space.

But in the meantime, parents are scrambling to come up with creative solutions.

Triple bunk beds are commonplace, as are family shower schedules in homes where everyone shares the same bathroom. One parent said her daughter slept in a narrow bedroom mostly taken up by a stairwell. Another said she hung curtains around each of her children’s beds in the room they shared, providing some privacy but giving the room a hospital-like feel.

Sarah and Peterson Almodovar, both 34, have created an Instagram account to document renovations they’ve made to the nearly 750-square-foot, rent-stabilized apartment in Washington Heights that Mr. Almodovar grew up in, and where the couple now lives with their three young children, who are 2, 3 and 6.

They store bikes and scooters in the trunk of their car so they don’t have to lug them up the stairs to their apartment on the fifth floor, and the whole family shares a single bathroom.

The couple said their affordable rent, which is under $1,000 a month, allowed them to stay in the city where they felt most at home.

“There’s so much that New York City, specifically, can give us,” Ms. Almodovar said, adding that as an interracial couple, she worries they will “stick out like a sore thumb” someplace else.

That’s not to say that the city’s dwindling number of families of five don’t sometimes attract curious stares, just by virtue of their size.

One father said the bags of laundry he hauled to the local laundromat were so hulking that he looked like Santa Claus on Christmas Eve. His family commutes via a cargo bike with three kids’ seats attached. One mother recalled years of pushing 100 pounds of children around — two of her children in a double stroller, with her third riding on a kickboard on the back.

Several parents said they announced their third pregnancies only to be greeted with questions from friends about when they were planning to leave the city.

Andrew Gounardes, a Democratic state senator from Brooklyn whose wife gave birth to their third child a few weeks ago, has long seen his Bay Ridge neighborhood as an idyllic, affordable place to raise a family.

But something has started to shift, said Mr. Gounardes, 40. Last year, four or five families in his son’s day care class left Brooklyn, all crossing the river to New Jersey.

He can understand why. His family may soon have to pay $6,000 a month to have all three children enrolled in day care.

The city, Mr. Gounardes said, is at risk of becoming “a place for people who can’t afford to go anywhere else, living two families in an apartment, or the very wealthy who can afford a brownstone worth millions of dollars. There’s nothing in between.”

That’s why some New Yorkers have decided they can’t afford the third child they might have wanted.

Rachel Birch has two boys, and there is a part of her that always wanted to raise a girl. Even though she and her husband both have good, well-paying jobs, their budget feels too tight for them to add to their family.

“The fact that we’re living paycheck to paycheck is bonkers,” said Ms. Birch, 41. “We don’t travel. We just bought our first car ever in our lives.”

If Ms. Birch’s younger son does not get a seat in the city’s free program for 3-year-olds next year, the couple will have to empty their savings to pay for his preschool. She worries about debt, and what might happen if someone in the family gets sick and they have to pay for unexpected medical bills.

For now, Ms. Birch and her husband are shelving the idea of expanding their family.

“We can’t even make the decisions we would want to make,” she said. “Because the decision has been made for us.”