A bigger glass lobby stretching into Lincoln Center’s plaza. Operas on Sunday. And perhaps, following the lead of its neighboring theaters recently renamed for David Geffen and David H. Koch, slapping another wealthy donor’s name on the storied Metropolitan Opera House.

These ideas, disclosed by Peter Gelb, the Met’s general manager, in an interview as he prepared to begin his 10th season at the helm of the company, suggest a renewed focus on drawing new audiences and raising desperately needed money for the opera, where attendance has struggled. If Mr. Gelb’s first decade was notable for technological innovations that broadened the Met’s reach outward — his popular “Live in HD” simulcasts of operas at cinemas reached 2.6 million people last season — much of what he would like to do in the coming seasons looks inward.

“The last thing that we can do is sit idly by,” Mr. Gelb said during the interview in his office. “We have to keep poking the tires and looking at new ways of approaching the art itself in the form of new productions and commissions, and also looking at the physical plant of the Met, and how we perform. We’re looking at everything.”

After several years of serious fiscal challenges, the Met’s recent cost-cutting — including from its artists and its workers, who agreed to their first pay cuts in decades last year after a series of bitter labor negotiations — is beginning to bear fruit. The company ended last season with a surplus of $1 million, according to preliminary financial results released on Wednesday; that was a marked improvement from the prior season, when it ran a $22 million deficit, its most serious in decades. And Mr. Gelb said that the Met had raised the first $100 million of a five-year, $600 million fund-raising drive aimed at doubling its endowment, supporting operations and paying for new capital projects, including the hoped-for renovation and expansion of its lobby.

But there was worrisome news on the attendance front: The Met said it had earned only 69 percent of its potential box-office revenue last season, down from 73.2 percent the previous season. That is one reason Mr. Gelb said he would like to add at least some performances on Sundays, initially on a trial basis. Met officials believe it would be the first time they have presented fully staged operas on Sundays. Other major opera houses and Broadway theaters hold Sunday performances, and Mr. Gelb said that the Met had seen its Friday and Saturday productions outsell weeknights in recent years as audience habits have changed.

“If you’re going to experience a three-hour, three-and-a-half-hour opera and want to have dinner, you need time,” Mr. Gelb said. “A Sunday performance would be something that would make a lot of sense.”

Significant hurdles remain for many of Mr. Gelb’s plans. Adding Sunday performances would require the agreement of the Met’s work force and its powerful unions, whose relationships with Mr. Gelb were badly strained during last year’s labor talks, and whose members already work punishing schedules during the opera season. Expanding the Met’s lobby into the Lincoln Center plaza would require successful fund-raising as well as the approval of the center’s administration and, possibly, the city. And traditionalists may shudder at the idea of a new name for the opera house, known for more than a century as the Metropolitan Opera — an internationally recognized classic along the lines of the Teatro alla Scala, the Royal Opera House or, closer to home, Yankee Stadium.

Mr. Gelb said that the Met needs to do these things, and more, to ensure that it can continue to thrive. One of his ideas — inspired in part by last season’s new production of “Pagliacci,” which featured a troupe of traveling vaudevillians — is to create an opera truck to bring small-scale, staged performances with a small orchestra to communities around New York. He has been working on the project, tentatively called “MET2GO,” with the Dutch director Lotte de Beer, who has an organization, Operafront, which does similar work in the Netherlands. Mr. Gelb, who is working to raise money for the project, hopes to have a traveling version of Verdi’s “La Traviata” ready by June 2016 or 2017.

“The Met can never be accessible enough,” he said.

Toward that end, he said, he wanted to make the Met more welcoming by expanding and renovating its cramped lobby — which the building’s architect, Wallace K. Harrison, was forced to scale back to save money half a century ago. “What was left was this very tight fit between the front doors of the Met and the entranceway, so in a period of 30 to 45 minutes before a performance you have this mob scene of people trying to get into the opera house,” Mr. Gelb said. “Which is good — at least people are trying to get in.”

The Met has engaged Levien & Company, a project management firm that has worked on other successful theater renovations in the city, to study how it might be able to build a low glass enclosure running the width of the Met and extending 30 or 40 feet into the Lincoln Center plaza. That addition would add several thousand square feet of space that would allow the Met to redesign its box-office area, gift shop and art gallery and to possibly add a cafe.

Jed Bernstein, the president of Lincoln Center, said that it would be premature to discuss the project. But, he said, “In general, I believe that things that are good for the Met are good for Lincoln Center.”

“Conceptually, is it a good idea for the Met to try to come up with creative and interesting new ways to engage with their audience?” he asked. “Absolutely. Would we want to support them in that? Absolutely.

“Does it make sense to do a specific thing, like do a glass extension to the Met? I don’t know, because we haven’t seen any idea of really what that would mean, or what that would look like, or any of those things.”

Capital projects are often more attractive to potential donors than equally needed campaigns to, say, increase endowments. The Met’s endowment fell dangerously low in recent years as the company withdrew money to help pay for its high annual operating costs. Those costs are now falling.

All told, the Met spent $310 million last season, down from $316 million the season before and $327 million two seasons ago. This year its budget calls for it to spend less than $300 million for the first time since 2010. Its endowment was valued at $266 million at the end of July, according to Mr. Gelb, but that figure does not include $19 million in pledged donations. The Met, which was drawing more than 8 percent of its endowment annually a few years back, has been steadily reducing that amount, from 6.5 percent in 2014 to 6 percent last season and this season; it plans to phase down to 5 percent by 2018.

Mr. Gelb said that as the fund-raising campaign proceeded, the Met would consider offering naming rights to the theater as a whole if a large enough donation were made. “We’re looking for a significant gift — a major gift that could somehow be associated with this front-of-house renovation and perhaps even the naming of the building,” he said.

Asked how large a gift would be required, he demurred. But he noted that the Met is larger and better known than its next-door neighbors — which were renamed for Mr. Koch and Mr. Geffen after they each donated $100 million.