With storage spaces filled with works that may never be shown, some museums are rethinking the way they collect art, and at least one is ranking what it owns.

Paintings line the basement storage space at The Indianapolis Museum of Art, which has graded its entire collection to help determine what art it may want to sell or transfer to another institution.

Paintings line the basement storage space at The Indianapolis Museum of Art, which has graded its entire collection to help determine what art it may want to sell or transfer to another institution. Lyndon French for The New York Times

Fueled by philanthropic zeal, lucrative tax deductions and the prestige of seeing their works in esteemed settings, wealthy art owners have for decades given museums everything from their Rembrandts to their bedroom slippers.

It all had to go somewhere. So now, many American museums are bulging with stuff — so much stuff that some house thousands of objects that have never been displayed but are preserved, at considerable cost, in climate-controlled storage spaces.

At the Museum of Fine Arts, Houston: ashtrays, cocktail napkins, wine glasses. At the Indianapolis Art Museum: doilies, neckties and women’s underwear.

In storage at the Brooklyn Museum: a roomful of home décor textiles, a full-size Rockefeller Center elevator and a trove of fake old master paintings the museum is barred from unloading.

Some collections have grown tenfold in the past 50 years. Most museums display only a fraction of the works they own, in large part because so many are prints and drawings that can only sparingly be shown because of light sensitivity.

“There is this inevitable march where you have to build more storage, more storage, more storage,” said Charles L. Venable, the director of the Indianapolis Museum of Art at Newfields. “I don’t think it’s sustainable.”

His museum was so jammed with undisplayed artwork that it was about to spend about $14 million to double its storage space until he abruptly canceled the plan.

Instead, it embarked on an ambitious effort to rank each of the 54,000 items in its collection with letter grades. Twenty percent of the items received a D, making them ripe to be sold or given to another institution.

The Indianapolis Museum of Art has ranked its collection with letter grades to determine which works may be a drain on resources. Which one do you think got an A? Choose Grade: C Cour d'une Ferme Maurice de Vlaminck c. 1926 Choose Grade: A Jimson Weed Georgia O’Keeffe 1936 Choose Grade: B The Flight into Egypt Marc Chagall 1943-44 Choose Grade: D Seascape A follower of Willem van de Velde II 17th century Right! Not quite. The Chagall won praise for its “whimsy and pathos,” but curators celebrated “Jimson Weed,” calling it O’Keeffe’s “largest and most ambitious floral work.” They noted, “The use of three blooms separates it in quality and importance among its peers of similar composition and subject.” “Seascape” earned its low grade in part because of a large hole in the canvas but also because it’s not by Velde, but a “follower of” Velde. In sum, a curator wrote: “Extremely poor condition. Poor quality painting.”

Not long ago, such ratings would have struck many in the museum world as crass. But Mr. Venable is now at the vanguard of a growing number of museum directors who are taking a hard look at how much they have and how they collect art because they fear a history of voracious stockpiling and the pressure to acquire still more is creating a crisis for American museums.

“It doesn’t benefit anyone when there are thousands, if not millions, of works of art that are languishing in storage,” said Glenn D. Lowry, the director of the Museum of Modern Art. “There is a huge capital cost that has a drag on operations. But more importantly, we would be far better off allowing others to have those works of art who might enjoy them.”

MoMA regularly culls its collection and in 2017 sold off a major Léger to the Houston art museum. Yet, it too is in the midst of yet another costly renovation (price tag $400 million) to be able to exhibit more of its ever growing collection.

Part of the problem is that acquiring new things is far easier, and more glamorous, than getting rid of old ones. Deaccessioning, the formal term for disposing of an art object, is a careful, cumbersome process, requiring several levels of curatorial, administrative and board approval. Museum directors who try to clean out their basements often confront restrictive donor agreements and industry guidelines that treat collections as public trusts.

Collections have ballooned in the past 50 years. Some major American museums have seen the size of their collections soar tenfold. Even the oldest institutions often saw their holdings double or triple in number. Brooklyn Museum 3% MFA Boston 75 Philadelphia Museum of Art 114 Denver Art Museum 251 Percent change in collection size, 1970 to present Indianapolis Museum of Art 265 Metropolitan Museum of Art 329 Whitney Museum 692 Dallas Museum of Art 818 SF MoMA 1,014 MFA Houston 1,438 100% 300 500 700 900 1,100 1,300 Major museums are only able to display a small portion of their collection. Number of objects on display at a given time Number of objects in storage 300,000 objects Dallas Museum of Art Whitney Museum 600,000 SF MoMA Indianapolis Museum of Art MFA Houston 900,000 Denver Art Museum Brooklyn Museum Philadelphia Museum of Art 1,200,000 MFA Boston 1,500,000 Metropolitan Museum of Art The percentage on display is affected by space constraints, but also by how much of a collection is devoted to works on paper, which cannot be shown for long due to light sensitivity. The Met collection is particularly weighted toward works on paper, but its percentage on display, about 4 percent, is in rough parity with other museums on the list. Percent of collection not on paper Percent on paper Metropolitan Museum of Art Whitney Museum SF MoMA Philadelphia Museum of Art MFA Houston MFA Boston Indianapolis Museum of Art Brooklyn Museum Dallas Museum of Art Denver Art Museum 0 20 40 60 80 100% Collections have ballooned in the past 50 years. Some major American museums have seen the size of their collections soar tenfold. Even the oldest institutions often saw their holdings double or triple in number. Brooklyn Museum MFA Boston Philadelphia Museum of Art Percent change in collection size, 1970 to present Denver Art Museum Indianapolis Museum of Art Metropolitan Museum of Art Whitney Museum Dallas Museum of Art SF MoMA MFA Houston 100% 300 500 700 900 1,100 1,300 Major museums are only able to display a small portion of their collection. Number of objects on display at a given time Number of objects in storage 300,000 objects Dallas Museum of Art Whitney Museum 600,000 SF MoMA Indianapolis Museum of Art MFA Houston 900,000 Denver Art Museum Brooklyn Museum Philadelphia Museum of Art 1,200,000 MFA Boston Metropolitan Museum of Art 1,500,000 The percentage on display is affected by space constraints, but also by how much of a collection is devoted to works on paper, which cannot be shown for long due to light sensitivity. The Met collection is particularly weighted toward works on paper, but its percentage on display, about 4 percent, is in rough parity with other museums on the list. Percent of collection not on paper Percent on paper Metropolitan Museum of Art Whitney Museum SF MoMA Philadelphia Museum of Art MFA Houston MFA Boston Indianapolis Museum of Art Brooklyn Museum Dallas Museum of Art Denver Art Museum 0 20 40 60 80% Collections have ballooned in the past 50 years. Some major American museums have seen the size of their collections soar. Even the oldest institutions often saw their holdings double or triple in number. Percent change in collection size, 1970 to present Brooklyn Museum MFA Boston Philadelphia Museum of Art Denver Art Museum Indianapolis Museum of Art Metropolitan Museum of Art Whitney Museum Dallas Museum of Art SF MoMA MFA Houston 200% 400 600 800 1,000 Major museums are only able to display a small portion of their collection. Number of objects on display at a given time Number of objects in storage 300,000 objects Dallas Museum of Art Whitney Museum 600,000 SF MoMA Indianapolis Museum of Art 900,000 MFA Houston Denver Art Museum Brooklyn Museum 1,200,000 Philadelphia Museum of Art MFA Boston Metropolitan Museum of Art 1,500,000 The percentage on display is affected by space constraints, but also by how much of a collection is devoted to works on paper, which cannot be shown for long due to light sensitivity. The Met collection is particularly weighted toward works on paper, but its percentage on display, about 4 percent, is in rough parity with other museums on the list. Percent of collection not on paper Percent on paper Metropolitan Museum of Art Whitney Museum SF MoMA Philadelphia Museum of Art MFA Houston MFA Boston Indianapolis Museum of Art Brooklyn Museum Dallas Museum of Art Denver Art Museum 20 40 60 80% By Alicia DeSantis | Numbers are self-reported by individual institutions.

And many still hold the view that a wholesale parting with objects can be risky. Overlooked art comes back in style. Forgotten treasures turn up. Many pieces, they argue, should be retained for scholars, regardless of how often they go on public view. And much art still needs to be acquired as museums respond to the soaring popularity of contemporary art and aim to integrate more work by women and artists of color.

“People can’t understand why museums have more than they can show at any given time,” said the critic and curator Robert Storr. “But preserving the best of the past — no matter how unpopular it may temporarily become — is the purpose of museums. They should protect their holdings; they shouldn’t jettison them for short-term gains or savings.”

But holding on to it all has consequences, most notably the pressure to build new exhibition wings. Some wealthy collectors take matters into their own hands, creating private museums to retain control of what goes on view.

Eli Broad, the philanthropist, said one reason he created his own Los Angeles museum, the Broad, was to ensure a proper display of his impressive collection of modern and contemporary art.

“I don’t see how giving art to museums that are not prepared to show a fair amount of it makes any sense,” Mr. Broad said. “Of the 2,000 works in our collection, I got the sense they would show 1 or 2 percent of the work and the rest would go in storage.”

Which one of these paintings from the Indianapolis Museum of Art was ranked a D? Choose Grade: B Fountain at the Villa Medici Maurice Denis 1904 Choose Grade: D Le Pont Neuf Merio Ameglio c. 1940 Choose Grade: B Entrance to the Port of Honfleur Paul Signac 1899 Correct! Sorry. Ameglio’s view of the Pont Neuf in Paris was painted several decades after the other two and found to be “mediocre” — and “more loosely brushed than his more structured paintings.” The Signac, on the other hand, was noteworthy, a curator noted, because it was the museum’s “only canvas by this key member of the Neo-Impressionist movement.”

Which one of these devotional sculptures was ranked a D? Choose Grade: A Crucifix Gaspar Núñez Delgado 1599 Choose Grade: A Christ at the Column Caspicara (Manuel Chili) 18th century Choose Grade: D Pieta Unknown 18th century You got it! Not quite. In this case, the curator’s D is based on the condition (“horrible”) and the aesthetics (“poorly executed.”) The higher-rated 16th-century crucifix was described as “quintessentially Spanish,” and the curator noted that its forms exhibited “wonderful articulation.” The 18th-century Christ figure was embraced because it was produced by a master of the celebrated Quito School — Ecuadorian artists working in the Spanish devotional tradition, here with “naturalistic effects” such as “glass eyes.”

Generous to a Fault?

The current museum storage predicament has its roots in gifts like Adelaide Milton de Groot’s to the Metropolitan Museum of Art. Upon her death at 91 in 1967, she did not give just a few paintings from her collection. She gave all of them — more than 200.

Thomas Hoving, then director of the Met, recalled in his 1993 book, “Making the Mummies Dance: Inside the Metropolitan Museum of Art,” that he was “shocked” to learn from his No. 2, Theodore Rousseau, that “only half a dozen paintings” were first-rate.

“Many of the other pictures were not even worth showing,” he wrote. Upset, Mr. Hoving said he demanded an answer from Rousseau, “What were we going to do with them?”

“Put them in storage or sell them was his answer,” he added.

Adelaide Milton de Groot, who died in 1967, arranged in her will to leave more than 200 paintings to the Metropolitan Museum of Art. Sidney J Waintrob; Budd Studio

Museums have always had to be diplomatic with important collectors. With acquisition budgets so limited, they have long depended on donors’ largess.

“Museums were accepting with less criticality when collections were smaller,” said James Rondeau, director of the Art Institute of Chicago. “We took 12 when we might not have even taken one.”

Some donors were able to dictate terms.

In 1985, when the philanthropist Wendy Reves donated more than 1,400 works from the collection of her late husband Emery Reves to the Dallas Museum of Art, she required that it re-create five rooms from their villa in the South of France — including furnishings from the décor of the home’s original owner Coco Chanel. Among the accouterments in the display: Mrs. Reves’ slippers beside the bed.

Four years ago, Stefan Edlis and Gael Neeson gave the Art Institute 42 contemporary works worth an estimated $400 million. It was the largest gift of art in the museum’s history and came with a stipulation: All the works have to be on display for the next 50 years.

“I got the deal of a lifetime,” Mr. Edlis said in an interview.

In the case of Ms. de Groot’s large gift to the Met, the museum sold some 50 pieces, and ended up with much public criticism and an inquiry by the Attorney General’s office as to whether the Met had trampled on the intent of Ms. de Groot’s will.

Two years later, Mr. Hoving agreed to accept the collection of the investment banker Robert Lehman — at 2,600 works, then the largest art donation in the Met’s history. Though some art critics questioned its quality, the Met built a wing to display the collection, with rooms that re-created the Lehman family residence.

Under the Lehman Foundation’s agreement with the Met, the collection will remain in the museum forever.

Today the Met’s collection tops 1.5 million items, many of them stored in 105,000 square feet of on-site storage, the equivalent of almost two football fields, and four off-site locations in New York and New Jersey.

Max Hollein, director of the Met, said the collection’s size reflects that the museum’s mission extends beyond display. “We also preserve the cultural heritage of humankind,” he said, but added that going forward, “Our focus at the Met is not going to be on what we still need but on what we have and how we display it.”

As Mr. Hoving found out, deaccessioning can sometimes be a dirty word. A routine practice, it is nonetheless often fraught with controversy. Won’t donors be insulted when museums re-gift or sell their donated work? Aren’t such gifts, underwritten by taxpayers, part of the public trust?

The Berkshire Museum drew protests when it announced a plan to sell art from its collection in 2017. Gillian Jones/The Berkshire Eagle, via Associated Press

Moreover, the Association of Museum Directors has strict guidelines dictating that proceeds from such sales can only be used to acquire more work, not to cover operating costs like staff salaries. Institutions that have violated these rules in the name of financial survival — including New York’s National Academy of Design, the Delaware Art Museum and the Berkshire Museum— have been labeled pariahs, in some cases penalized by the refusal of other institutions to lend works.

“If an institution is faced with an existential threat, isn’t it better for the institution to survive with some works of art than no works of art?” countered Gary Tinterow, director of the Museum of Fine Arts, Houston, defending the Shelburne Museum in Vermont’s decision to sell $25 million worth of art in 1996. Mr. Tinterow said his museum has gradually been getting rid of the excess in its two house collections of decorative arts — including those ashtrays and stemware.

Anne Pasternak, the director of the Brooklyn Museum, said there is increasing discussion these days about revisiting the strictures of deaccessioning policies. But she acknowledged “there is a lot of fear around this conversation.”

The Indianapolis museum rated one of these landscapes, all by the same artist, a C and sold it. Can you guess which one? Choose Grade: C The River Theodore Clement Steele 1906 Choose Grade: B The Bloom of the Grape Theodore Clement Steele 1893 Choose Grade: B Winter in Munich Theodore Clement Steele 1885 That’s correct! Sorry. With some 20 other landscapes by Steele, the museum decided to part with “The River,” which curators found “redundant and not one of Steele's best pictures.” Museums often deaccession surplus works. The other two paintings did not rank as “premier” representations of work by Steele, whose “command and use of light” in landscapes is considered masterly. But the curators noted that both were made by a celebrated painter from Indiana and keeping them would help maintain the comprehensiveness and quality of the museum’s holdings by artists from the state.

Two of these paintings of Roman ruins are ranked A, but one is a C. Can you guess which one? Choose Grade: C Ruins With the Temple of Antoninus and Faustina A follower of Giovanni Paolo Panini c. 1727-1730 Choose Grade: A Roman Capriccio: The Colosseum and Other Monuments Giovanni Paolo Panini 1735 Choose Grade: A Roman Capriccio: The Pantheon and Other Monuments Giovanni Paolo Panini 1735 Right! Not quite. The lower-ranked painting is by a follower of Panini, and the curators noted that it was “not as high quality” as others by the artist himself that the museum has on view. Panini was known for his atmospheric views of Roman monuments, often painted alongside each other in imagined settings. These works were often sold to aristocrats traveling through Italy to complete their classical education with a so-called Grand Tour.

From Dusty Attic to Modern Museum

From the Brooklyn Museum’s first days, storage was an issue. When its Beaux-Arts building on Eastern Parkway was built in 1893, the museum was focused on amassing enough art to put on view, not where to keep it.

“They took just about anything that was offered and thought maybe someday it will be useful,” said Kevin Stayton, the museum’s chief curator emeritus.

In those early years, random spaces were recruited to house things. “You had storerooms and you threw work in it,” Ms. Pasternak said.

Some donors literally dropped their collections at the door. One art dealer, Ivan C. Karp, persuaded the museum, starting in the 1950s, to take some 400 fragments of ornate terra cotta and stone mythological creatures that he and friends had salvaged from demolition sites. They were stored in the museum’s backyard. Some were used for a sculpture garden. Others ended up in a parking lot.

Objects stored in remote areas came to be forgotten. Such was the case about 20 years ago, when curators found an old slab of marble leaning against a back storage wall. It was a delicately carved 1860s relief by an important self-taught sculptor, Margaret Foley.

Arnold Lehman, who led the museum from 1997 to 2015, recalled confronting the great morass, including more than 23,000 items of American and European clothing and accessories, an impressive but fragile collection that was costly to maintain.

One advancement in storage has been to make it visible to the public as done here in the Brooklyn Museum's Luce Center for American Art. Andrea Mohin/The New York Times

“I kept saying that we weren’t equipped to deal with this properly,” Mr. Lehman said.

He set out to consolidate and now the museum is that rare art institution that holds fewer items today than it did 10 years ago.

Not that it was easy.

Some complained when Mr. Lehman transferred some 1,500 terra-cotta pieces to a foundation in St. Louis. There was grumbling when he sent the museum’s huge trove of costumes to the Met in 2008 under a deal that gave Brooklyn continuing access, and its name on the collection.

Mr. Lehman was never able to unload some of the 926 items that were bequested by Col. Michael Friedsam, once president of the department store B. Altman, who died in 1932.

A quarter of the gifts, including old master paintings, turned out to be fake, misattributed or of poor quality. The museum still stores and cares for them because the courts have ruled that, under the colonel’s will, deaccessioning requires permission from his executors. The last of them died in 1962.

The Brooklyn Museum storage facilities are updated today. Paintings hang on special racks; objects returning from loan are temporarily isolated, lest they be carrying pests; and an open storage area allows visitors to see items that would otherwise be out of view.

But Ms. Pasternak, who took over as director in 2016, is continuing to look at “next steps” regarding storage. One focus: a room that holds thousands of textiles, European tapestries and lace, and some furniture.

She would like to turn it into a gallery for African art. The cost-benefit analysis, she said, seems straightforward: “A permanent home for an African art gallery versus storing something that we’ve never shown.”

The Indianapolis Museum of Art at Newfields has deaccessioned more than 4,600 works since beginning a major study of its collection in 2011. Lyndon French for The New York Times

On the Front Lines: Indianapolis

If you want to start an argument, there are few better ways than assigning something a grade.

So Mr. Venable created quite a stir by deciding to rank the entire collection of his Indianapolis museum.

Founded in 1883, the museum shows 8 to 10 percent of its collection at any one time. The ranking began in 2011 when a Mellon Foundation grant paid for outside experts to spend six years reviewing the collection.

His own staff then built on that work. By the end every item had a grade: “A being a masterpiece,” Mr. Venable said, “and D being maybe onetime in the distant past this was a valuable object for us but we probably shouldn’t hang on to that.”

The assessment measured a work’s aesthetic qualities, its physical condition and whether the museum perhaps had better examples of the genre. Mr. Venable decided not to keep art purely for study, asking. “How many scholars actually look at those things on an annual basis?”

Now comes the tough part — getting rid of the works through sale or transfer to another institution. What may be a D painting to a large, encyclopedic museum, which has several by that artist, may be an A to a smaller institution, which has none.

Charles L. Venable, director of the Indianapolis Museum of Art at Newfields. Lyndon French for The New York Times The storage spaces at Indianapolis. The conservation of art requires an understanding of aesthetics, logistics, the science of materials and how they react over time and to other substances. Lyndon French for The New York Times

Since 2011, the Indianapolis museum has deaccessioned 4,615 objects, with the vast majority of those having been sold. Some 124 works have been transferred to other institutions, including art glass from the Marilyn and Eugene Glick Collection.

The museum decided that only some of the collection’s 250 pieces were worth keeping, so Mr. Venable approached the Glicks' grandson-in-law, David Barrett — a museum trustee — about transferring some to another institution.

The Marilyn K. Glick Center for Glass at Ball State University in Muncie, Ind., soon received 60 pieces from Indianapolis.

That kind of flexibility is essential to museum survival going forward, Mr. Venable said.

”What is the balance between almost obsessively art collecting and spending vast amounts of resources on it?” he said. “Are we really just addicts collecting objects that our curators bring in generation after generation?”

Peter Libbey contributed reporting.

Quiz produced by Gabriel Gianordoli and Josephine Sedgwick. Graphics by Sarah Almukhtar and Alicia DeSantis.

Quiz images from top: Maurice de Vlaminck/Artists Rights Society (ARS), New York; Indianapolis Museum of Art at Newfields, Georgia O’Keeffe Museum/Artists Rights Society (ARS), New York; Indianapolis Museum of Art at Newfields, The Estate of Marc Chagall/Artists Rights Society (ARS), New York/ADAGP, Paris; Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Maurice Denis/Artists Rights Society (ARS), New York; Indianapolis Museum of Art at Newfields, Merio Ameglio/Artists Rights Society (ARS), New York; Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art, Indianapolis Museum of Art at Newfields, Indianapolis Museum of Art at Newfields.