Animal advocates and agency officials alike said new shelters could go far to alleviate overcrowding and check the spread of disease.

“We really welcome the day that those two shelters are built,” Risa Weinstock, the executive director of Animal Care Centers, said. “In the meantime we still have those challenges. But we’ve proved that we’re an organization worth investing in.”

Since 2007, the city has increased Animal Care Centers’ budget to about $13 million from $7 million.

In an interview, Ms. Weinstock described how the money had been put to use: new “mobile adoption centers” — vans from which more than 700 animals were adopted last year; a food pantry for pets in the Bronx; a behavioral staff of 22 that, among other things, runs the playgroups, which the shelter says improve the dogs’ immunity and make them more docile and adoptable when they return to their kennels. (Coming soon to the backyard run in Manhattan: artificial grass.)

Ms. Weinstock said the shelters had also added admissions counselors who, since 2014, have persuaded about 1,700 owners to keep their pets rather than surrender them by connecting the owners with medical grants, low-cost boarding or behavioral advice. “So often,” she said, “people come in and think that’s their only option.”

The agency has worked on its image as well. Last year it changed its name, though it does not yet have the money to alter its signs.