The serial residency of her grandchildren meant Esta could live in her beloved house longer than would have been feasible, Mr. Goldman said. Soon after, he moved out and so did she — to an assisted living facility near Albany, N.Y. She died in 2020.

The grandchildren know they have a good deal and try to hold up their end. Mr. Kantor runs errands, sees that insurance is kept up-to-date and recently took the lead in hiring an aide for his grandmother. During her five years in residence, Ms. Zuniga helped with the grocery shopping and laundry; because her grandparents are not fluent in English, she would speak to the building superintendent and landlord on their behalf.

Ally Iseman, who is 5-foot-11, does all the reaching and climbing up stepladders for her grandmother, June, who is a foot shorter. Ms. Shiffer takes her grandmother to doctors’ appointments. “I don’t always understand the doctors,” her grandmother, Ms. Ingraham, 89, said. “Meghan explains what it all means.”

Value added, Ms. Ingraham continued, is the window into a changing world. “I realize I’m of one generation, and because of Meghan I’m having an opportunity to gain firsthand knowledge of how this new generation thinks and functions,” she said. “And you know, that’s a blessing.”

Internecine battles have been all but nonexistent.

In most cases, disagreements between the grandparents and grandchildren have been minimal to nonexistent, according to all those interviewed. “Amazingly, no head-butting,” Mr. Elson said. His granddaughter concurred. “There’s just a different relationship with grandchildren. And now, it’s grown-up to grown-up,” Mr. Elson said. He did admit though, that his granddaughter, now back in Washington after completing the coursework for her degree, “was not quite as neat as one might wish.”

June Iseman extends her sympathy. “I just keep the door to Ally’s room closed,” she said.

A few months ago, Ms. Zuñiga, now 23 and an information technology engineer, moved to an apartment in South Williamsburg with two friends. She stops by her grandparents’ place almost every weekend to see if there are groceries to fetch or clothes to take to the laundromat.

“The first time I visited after I moved out, my Gramma got a little teary-eyed when I left,” she said. “And I was like, ‘I’ll be back!’”