For every group of budding musicians that get together to form a rock band, there seem to be almost as many classical groups these days doing the same.

One of the most popular ensembles to form is the string quartet, which has a vast and beautiful repertoire at its beck and call. A string quintet, with two violas along with the two violins and cello, is a bit rarer, but there is still a good deal of great music already written for that combination.

But a string quintet with a double bass added to the usual two violins, viola and cello, is something else again.

This Sunday, the New York-based Toomai String Quintet, which has just that lineup —quartet plus bass — comes to town for a return engagement with the Miami Civic Music Association. The group will focus on two icons of Latin American music: Mexican composer Manuel Ponce and Cuban composer Ernesto Lecuona.

Andrew Roitstein, the Toomai’s bassist and co-founder along with violist Erin Wight, said the quintet was formed in 2007 when the two were in graduate school at Juilliard and had been playing a good deal of contemporary music. They assembled the first version of Toomai for a competition for a residency at New York’s 92nd St. Y, and won.

“There’s very little standard repertoire for this instrumentation, but we really enjoyed it because it offers a different kind of sound world than the string quartet,” Roitstein said. “Basically, we just really clicked as a group.”

The quintet, which takes its name from a Rudyard Kipling character (Toomai of the Elephants, from “The Jungle Book”), has had personnel changes since then, but all of its current members are alumni of the Juilliard or Manhattan schools of music, and range in age from 26 to 29. Along with Roitstein and Wright, the quintet includes violinists Emilie-Anne Gendron and Pala Garcia and cellist John Popham.

From the beginning, finding repertoire to play was a challenge, but Roitstein said the group built up a considerable repertoire that includes some standard repertoire (works by Dvorak, Boccherini and French composer George Onslow), four- or five-pieces world premieres and about 20 arrangements written by Roitstein.

“That’s one thing we really like about this instrumentation, in that it kind of demands that we get creative about how we get new music. It’s an artistically fulfilling process because we have to start from scratch a lot of the time,” he said.

Sunday’s program includes the third movement of a string quartet for violin, viola, cello and bass by the Mexican composer Carlos Chavez, the contemporary Mexican composer Mario Lavista’s Reflejos de la Noche, and Ponce’s Suite Cubana, in an arrangement by Roitstein. Ponce also will be represented by his Tres Canciones Mexicanas, which includes Estrellita, very familiar as a violin encore.

For the Cuban part of the program, there will be arrangements of three Lecuona songs — Zambra Gitana, En Tres por Cuatro and A la Antigua — plus five popular Cuban songs sung by Roitstein’s sister Alina, an operatic soprano who also sings salsa and Brazilian popular song. She’ll sing Cachao Lopez’s A Gozar con mi Combo, Benny Moré’s Bonito y Sabroso, Antonio Castro’s No Encuentra Palabras, Ernesto Duarte’s Como Fue and Obdulio Morales’ Dame Bururu. [Here’s a video of Moré singing Como Fue.]

Roitstein, 28, grew up in Los Angeles, but his parents are Miamians, and his mother is originally from Cuba. His father, a jazz pianist, also plays in a salsa band, and Roitstein grew up listening to Cuban music from his earliest years. He also has spent a good deal of time in Mexico, where one of his grandmothers retired and where he taught and played chamber music.

“It’s been a fun program for us, because one of the first things we did as a quintet was … ‘A Gozar con mi Combo.’ So one of the first things we started doing was popular Cuban dance music with string arrangements,” he said. “It’s evolved, and we’ve been developing a big repertoire.”

The two central composers of the program, Ponce (1882-1948) and Lecuona (1895-1963), are iconic in their home countries and share career similarities, Roitstein said.

“They both studied in Europe, and they both came back,” he said, where they developed nationalistic styles of composition. “Lecuona looked to a lot of Afro-Cuban rhythms and incorporated them into his songs, and Ponce wrote these folky melodies that are really melodic and beautiful. We wanted to look at those two composers and the legacy they left to composers who followed after them.”

Toomai’s original mission was to mount interactive concerts for young people, and that still makes up much of its work. It has a residency at a New York hospital through the agency of Carnegie Hall, and regularly visits schools, and in both cases the members engage in dialogue with their audiences about the music they’re playing.

Next month, Toomai does a tour of Los Angeles, and will bring this very same program to the Museum of Latin American Art in Long Beach. They also will present a program of contemporary music, including a commissioned piece by New York-based Vincent Raikhel, and will do its interactive concerts for students throughout Southern California, he said.

Toomai, which is hoping to raise enough money to do some recording next year, benefits from today’s eclectic music scene, in which old barriers and genre restrictions have loosened considerably. Its members have distinctly different tastes, and its concerts reflect that.

“A lot of us are avid about the contemporary music scene in New York, and because of that, we’re really passionate about premiering new works for the instrumentation because we just want to play new music,” he said, adding that its popularly oriented selections have include Roma songs as well as the Latin American pieces. “It’s a mix of everybody’s different influences, and we try to include that in all the concerts.”

That doesn’t mean that the older repertoire is pushed to one side, though.

“We do play a lot of classical music still,” Roitstein said. “It’s just that the palate is a lot more open right now.”

The Toomai String Quintet appears at 4 p.m. Sunday at Gusman Hall on the campus of the University of Miami in Coral Gables. Tickets are $25. Call 877-733-3031 or visit www.miamicivicmusic.org.