The musical “Rags” feels as though it could be a sequel to “Fiddler on the Roof” — and there’s an excellent reason for that. After he wrote the book for “Fiddler,” librettist Joseph Stein contemplated what might have happened to characters like those in “Fiddler” if they immigrated to America.

The result: “Rags.” Set in 1910 New York City, the show focuses on a young woman who flees the pogroms in Russia for the U.S.

“Rags” premiered on Broadway in 1986; it ran just four performances, following 18 previews. And yet it managed to nab five Tony nominations, including one for best musical.

A new version of “Rags” is being staged at Goodspeed Opera House — and we do mean new. The creative artists behind the show have revisited the piece for this production, and it’s a major overhaul. They wanted the chance to really pull the musical apart and reimagine it.

The forces behind “Rags” are a legendary lot. The lyrics are by Stephen Schwartz, who wrote the music and lyrics for “Wicked” and “Godspell.” “Rags’” composer is Charles Strouse, who did the music for “Annie” and “Bye Bye Birdie.” Stein died in 2010, but David Thompson (“The Scottsboro Boys,” “Steel Pier”) revised the book for the Goodspeed version.

Directing the production is Rob Ruggiero, the artistic director of TheaterWorks in Hartford who has helmed nine exceptional productions at Goodspeed.

This fresh “Rags” has made many changes, including dropping characters and songs, but what’s vital isn’t so much what has been altered but how it works. It’s cohesive and, more important, it’s moving. It seamlessly shifts among its subplots, propelled by appealing songs. (The songs benefit from Schwartz’s smart and witty lyrics, and Strouse’s music touches on various styles, from faux Italian opera to ragtime to religious ceremonials.)

The storyline is all about trying to make a better life, about facing obstacles — in short, about being human.

“Rags” is at its most effective when reflecting the modern echoes in this show set nearly 100 years ago. A story centering on the difficulties and possibilities of being an immigrant is, of course, terribly relevant today. As an audience member, you share the angst as the main character, desperate to escape the danger in her Russian homeland, tries to quell her panic as an Ellis Island guard turns her away. It’s chilling, too, when rich-and-privileged American characters sing about the new arrivals in a number that is bluntly titled “Take Our Country Back.” Sound familiar?

At the show’s close, images of real immigrants cycle through on a scrim. When the photos moved forward in time, eventually depicting 21st-century people, I initially thought it was unnecessary and too on-the-nose. But then I found myself tearing up, so it clearly had its intended impact.

As part of the reworking of “Rags,” the focus is primarily on Rebecca Herskowitz (played by Samantha Massell), who has come to the Lower East Side with her young son, David (Christian Michael Camporin). She ends up living with the family of a girl she met on the voyage to the U.S. They do piecework, and Rebecca, who can sew like a dream, joins them.

Her expertise at design catches the eye of factory owner Max Bronfman (David Harris, giving humanity to a figure who could be played as a moneyed, entitled stereotype), and they begin to sell her dresses to wealthy women.

At the same time, Rebecca sets off sparks with a labor organizer named Sal.

Massell, who resembles Katharine McPhee, imbues Rebecca with a quiet strength. She sings with grace and power, even if the big ballads she gets aren’t quite as distinctive and stirring as you might hope.

Sean MacLaughlin nicely balances Sal’s serious political intent with a charming playful side. MacLaughlin’s voice is impressive, powering the operatic extravagance of “Meet an Italian” and nuancing the romanticism of “Blame It On the Summer Night” with Massell.

Arguably the two most potent performances in “Rags” are, coincidentally, by two actors who starred in Goodspeed’s 2014 production of “Fiddler on the Roof.” Adam Heller, who was Tevye in “Fiddler,” portrays Avram Cohen, a Russian Jew who came to America, and, boy, can he finesse comic dialogue. Granted, his character is blessed with some of the show’s best lines, but, even so, Heller knows how to get the best out of them while still being understated.

Lori Wilner is his perfect match. She played Golde in “Fiddler,” and here she is the wise and wisecracking woman who sets her cap for Avram.

While much of the duo’s interplay is light, it deepens into heartwrenching emotion as tragedy falls. All along the way, though, the actors enjoy a wonderful chemistry. You’ll wish the couple — the performers as these characters — could star in their own show.

When it comes to the world these characters inhabit, the set designed by Michael Schweikardt is a clever construct. The central tenement is tiny, and its two rooms sit on the equivalent of a giant turntable so that they can rotate on the stage, bringing one room to the front as a given scene requires. Schweikardt uses historic photos as a projected backdrop, and that melds the real history with the fictional tale in a masterful way.

If you go

What: “Rags" 

Where: Goodspeed Opera House, 6 Main St., East Haddam

When: Runs through Dec. 10; 2 and 7:30 p.m. Wed., 7:30 p.m. Thurs., 8 p.m. Fri., 3 and 8 p.m. Sat., and 2 p.m. Sun.; also performances at 2 p.m. on select Thursdays and 6:30 p.m. on select Sundays

Tickets: Start at $29

Contact: (860) 873-8668, goodspeed.org