Almost as soon as the Museum of the City of New York opened at its current site in 1932, the trustees began discussing an addition. This summer, the dream, at long last, will come true.

With the 23,000-square-foot addition to the Georgian Revival building, designed by Joseph Freedlander — an underrated architect whose other works include the Bronx County Building (1931-35) and the Andrew Freedman Home (1924), both on the Grand Concourse in the Bronx — comes an ambitious attendance goal: increasing the number of museum visitors to 500,000 from 200,000 annually. The institution is recommitting itself to its original mission, which was to be the “people’s museum.”

That mission dates back to 1923. The museum, opening the following year in Gracie Mansion (which would become the official mayoral residence in 1942), was the brainchild of the New York historian Henry Collins Brown. Brown was a Scottish immigrant whose work as an advertising salesman sent him all over a city he grew to love as only a transplanted person could. He went on to write about New York history and buildings for The New York Sun under legendary editor Charles A. Dana. Brown also wrote numerous popular and charming books on New York history, including “Fifth Avenue Old and New” (1924) and “Brownstone Fronts and Saratoga Trunks” (1935). But he is best remembered for founding the Museum of the City of New York. He wanted to create an alternative to the New-York Historical Society, which was dedicated as much to national as to local history, lacked the populist appeal Brown sought, and was as much a historical research institution as a museum.

As it readies its new addition, which is slated to open in June, the Museum of the City of New York has delivered the message that it’s digging in on Fifth Avenue between 103rd and 104th streets; the museum no longer seeks to move downtown. It’s decided to stay put and grow — “to succeed, to thrive, to do more than prevail,” the museum’s director, Susan Henshaw Jones, said.

The addition may be small, but the statement it makes is large: “It’s simply a new beginning,” Ms. Jones, who came to the Museum of the City of New York in 2003 after serving as director of the National Building Museum in Washington, said.

In 2000, Mayor Giuliani told the museum it could move into the restored Tweed Courthouse, on Chambers Street, just behind City Hall. Fifth Avenue at 103rd Street was off the beaten path for museumgoers. But early in his administration, Mayor Bloomberg scotched the idea. He wanted the Tweed Courthouse for the Department of Education.

Back in the late 1980s, before the Tweed Courthouse came into the question, the museum had commissioned Polshek Partnership Architects, one of the city’s most prominent architectural firms, to plan a large addition to the Fifth Avenue building. The museum, alas, did not have the resources to go through with the plan. Once a downtown move seemed highly unlikely, Ms. Jones decided to contact the Polshek firm again. This time she asked for a modest addition onto the rear of the museum.

All earlier expansion plans have targeted the rear yard, open to both 103rd and 104th streets, between the museum and P.S. 171, a lovely 1905 school building by C.B.J. Snyder. The five-story school was built with a large, blank west wall, on the assumption that a similarly scaled building would one day abut it. Previous museum expansion plans would have obscured that ugly wall. But cost constraints called for an addition that could not possibly fill up the space. I am generally wary of aggressive Modernist additions to buildings in traditional styles. But I think the Polshek firm has done just about the only thing that could be done in this case. In the 1980s expansion proposal, the Polshek firm offered a more contextual design. At the present scale, I doubt very many architects could have pulled off a contextual design for what is, essentially, a modest pavilion placed in the center of a courtyard made problematic by the presence of the school’s huge blank wall. The Polshek firm’s solution was the sensible one: to create, in effect, a piece of sleek modern sculpture out of glass walls and delicate aluminum ribs. The addition will extend the main floor (which is entered up the steps from Fifth Avenue), creating the museum’s first climate-controlled gallery space. Phase 2 of the $80 million project will thoroughly renovate and modernize the systems of the 1932 building. The entire project is expected to be completed by 2012.

Much is made of how old museums need to retrofit themselves with glassy Modernist additions so as to be more welcoming to the public. I don’t get that at all, and would like to see the studies or focus-group surveys that suggest as much. Freedlander’s Depression-era design for the Museum of the City of New York is a jolly building. Though set well back from the street line, it expresses nothing of the pomp and ceremony museum boards seem to fear so much nowadays. It was, in fact, a 1930s version of a highly welcoming public building. Have our standards of public welcome changed that much since then?

Such questions in the end do not really apply to the present addition, which is the right thing.

As for the museum’s exhibitions, the recent “Robert Moses and the Modern City” was nothing less than a blockbuster — not to say superb — as an exhibition. It perfectly expressed the museum’s mission, which Ms. Jones says is the celebration of “our heritage of diversity, opportunity, and perpetual transformation.”