Broadway has been upended, but the Metropolitan Opera has yet to miss a performance.

The Omicron variant has toppled a slew of Broadway shows, disrupted dance productions, postponed festivals, forced the cancellation of dozens of concerts, and closed the mighty Vienna State Opera for almost a week. But it has yet to stymie the Metropolitan Opera, the largest American performing arts organization, which has not missed a performance this season.

Undaunted by the sharp rise in coronavirus cases, the Met has staged more than three dozen performances since late November, including productions of “Tosca,” “The Magic Flute,” “Cinderella” and “Rigoletto.” More than 3,000 people, who wore masks and showed proof of vaccination, filled the auditorium on New Year’s Eve.

Rehearsals are in full swing for another two dozen performances this month, each involving hundreds of people: solo singers, orchestra players, chorus members, dancers, actors, stagehands, follow-spot operators, dressers and makeup artists, among many others.

“We’re doing everything we possibly can to keep the Met open,” Peter Gelb, the company’s general manager, said in an interview. “I’m determined not to cancel a performance.”

The Met’s success so far in managing the surge can be attributed to a number of factors: strict health protocols, a robust system of understudies, the advantages that come from its structure as a large repertory company that mounts a different opera each day — and, to be sure, a dose of luck.

“There’s a sense of, ‘We can do this!’” said Sarah Ina Meyers, who directed the revival of “The Magic Flute,” which completed a nine-performance run on Wednesday with the help of far more cover artists than usual. “We’re trying to lift each other up.”

Still, Meyers added, after weeks of grappling with last-minute cast changes, drafting and then tearing up plans, “there is profound hope that we can go back to the normal level of crazy.”