New York City is once again expanding Mayor Bill de Blasio’s signature school-integration program, which tweaks the enrollment process at a few dozen schools to boost their diversity.

This year’s additions — which bring the total number of schools to 42, compared to 7 when the program launched in 2015 — include highly selective schools such as Bard High School Early College in Queens, where students earn an associate’s degree in addition to a high school diploma, and P.S. 77 The Lower Lab School in Manhattan, which only enrolls students who qualify as gifted based on the city’s entrance exams.

Also, for the first time, the “Diversity in Admissions” initiative is expanding to include a school in the Bronx: Academy of Applied Mathematics and Technology in Mott Haven.

The program affects a tiny fraction of city students and only a small number of the city’s almost 2,000 schools. It doesn’t alter system-wide policies that contribute to segregation, including the way most students are assigned to the school closest to their home. But it’s popular with individual schools, and has been one of the most tangible steps taken by the de Blasio administration toward addressing segregation in New York City, which is one of the most segregated school districts in the country.

Officials announced the latest expansion on Tuesday, two days ahead of a city council hearing on school diversity.

Among the added schools are all 16 traditional public elementary school in District 1. City leaders previously announced an intention to include all the elementary schools in the district, which spans the Lower East Side, East Village and some of Chinatown.

Deputy Chancellor Josh Wallack called the initiative a “key part of our schools better reflecting the diversity of our city.”

“We believe all students benefit from diverse and inclusive classrooms, and are excited to see our Diversity in Admissions initiative expand,” he said in an emailed statement.

Integration advocates have been lukewarm about the initiative. Matt Gonzales, who lobbies for school integration efforts with the nonprofit New York Appleseed, said any progress is important but that advocates still want to see more systemic changes.

“This is in no way impacting all 1.1 million students,” he acknowledged. “But it is creating more access for students right now.”

He added: “Obviously that needs to be built into a larger framework and set of priorities to promote more integrated schools all over,” the city.

Schools that join the Diversity in Admissions program are allowed to set aside a percentage of seats for students who meet certain criteria, such as qualifying for free or reduced-price lunch. The aim is to create or maintain a diverse mix of students by giving some an extra chance at being admitted.

The program sets targets for schools, but meeting those goals often requires outreach to ensure a diverse applicant pool. Most schools that have participated have met their targets when it comes to making offers for admission, according to education department figures.

Many schools in the program are located in gentrifying areas, where an influx of higher-income families has started to change the makeup of the local schools. The program can help stabilize the schools’ populations, so that they maintain a mix of students from different income levels.

For example, in Manhattan’s District 6, which is one of the city’s poorest, Muscota New School will set aside 30 percent of seats for students who qualify for free or reduced price lunch or live in temporary housing.

Principal Camille Wallin said the school — which is located in Inwood, a traditionally working class neighborhood where more families and young professionals have begun to settle — decided to join the initiative after noticing a significant drop in the number of needy students enrolled. For the 2016-2017 kindergarten class, only 19 percent of students qualified for meal assistance — down from 30 percent the previous year.

“Our belief system is that children learn from and with other children,” she said. “Widening the circle of people, and the experiences, and the social context of our school can only enhance the learning.”

The new batch of schools also includes P.S. 452 on the Upper West Side, which was at the center of a recent rezoning battle to relieve overcrowding and create more student diversity in Manhattan’s District 3. The school will first admit students living within the school’s attendance zone. For all remaining seats, students who qualify for free or reduced-price lunch will have priority.

Schools have to apply to join the initiative, and some are setting aside only a small number of seats. At Lower Lab, for example, 12 percent of seats will be set-aside for students who qualify for meal assistance. Last year, only 4 percent of students were considered poor.

At Bard in Queens, students who qualify for meal assistance will receive priority for 63 percent of seats. About 42 percent of students last year were considered poor.

Advocates say changing student assignment policies is only one part of integrating schools. The city should also focus on creating welcoming environments within schools by training teachers in culturally relevant practices and making sure school staff reflect the diversity of students, they say.

“Integration can’t happen without one or the other,” said Hebh Jamal, a member of the student-led advocacy group IntegrateNYC.

Here are the latest schools to join Diversity in Admissions:

P.S. 77 The Lower Lab School in Manhattan – Students eligible for free or reduced price lunch receive priority for 12 percent of seats. The standard district Gifted and Talented admissions criteria still apply.

P.S. 452 in Manhattan – For any seats remaining after all in-zone students are admitted, those eligible for free or reduced price lunch will receive priority.

P.S. 125 Ralph Bunche in Manhattan – Students eligible for free or reduced price lunch and those who are learning English receive priority for 60 percent of seats.

Muscota New School in Manhattan – Students eligible for free or reduced price lunch and students in temporary housing receive priority for 30 percent of seats.

Washington Heights Expeditionary Learning School in Manhattan – Students eligible for free or reduced price lunch and students in temporary housing receive priority for 75 percent of seats.

District 1 elementary schools in Manhattan – Students who qualify for free or reduced price lunch, are living in temporary housing or are learning English will have priority for 67 percent of seats. Those with disabilities will also receive a priority for kindergarten admissions. Students who do not meet those criteria will have priority for the remaining 33 percent of offers.

M.S. 260 Clinton School for Writers & Artists in Manhattan – Students eligible for free or reduced price lunch receive priority for 17 percent of seats.

Academy of Applied Mathematics and Technology in the Bronx – Applicants currently attending the following District 7 elementary schools receive priority for up to 25 percent of seats: P.S. 1, P.S. 49, P.S. 154, P.S. 277, P.S. 359, P.S. 369. Applicants currently attending the following District 7 elementary schools receive priority for up to 15 percent of seats: P.S. 5, P.S. 18, P.S. 25, P.S. 29, P.S. 31, P.S. 157, P.S. 161

Boerum Hill School for International Studies on Brooklyn – Students eligible for free or reduced price lunch receive priority for 40 percent of seats.

Bard High School Early College in Queens – Students eligible for free or reduced price lunch receive priority for 63 percent of seats.