Kennedy Center unveils plans for more comedy amid discussions about the future of “Shear Madness.” (Matt McClain/FOR THE WASHINGTON POST)

Move over, “Shear Madness.” After a mind-boggling 28 years as the money-minting chief tenant of a coveted performance space in the Kennedy Center — a uniquely advantageous perch in the world of nonprofit theater — the show is having its future there reassessed.

Officials of the center say they will be meeting next month with the play’s commercial producers to discuss what they describe as “the mixture of presentations” that they will now seek to feature in the penthouse space, the Theater Lab, that “Shear Madness” has occupied since 1987.

“We’re getting together with them in December, so I will have some more news in mid­December,” said Robert Van Leer, the center’s recently installed senior vice president for artistic planning. “This is a matter of working out the pieces of the puzzle.”

The prospect of a diminished calendar at the Kennedy Center for “Shear Madness” — which just last month for the first time established a New York franchise — is indicated in the expanded plans for comedy programming that the center announced Wednesday. Next summer, the center says, the play will go on hiatus, and the Theater Lab will be turned over to Chicago’s Second City, which has not performed at the institution in nearly two decades. Though the nature of “Shear Madness’s” tenancy after that remains unclear, the center says the play will return for some length of time in “early fall” 2016.

The renowned comedy troupe’s show, “The Second City’s Almost Accurate Guide to U.S. History,” is a new piece commissioned by the center that will run in the lab from June 19 to July 31. The production will be a centerpiece in a wide-ranging roster of comedy events running in the spring and summer. They begin in April in the Kennedy Center Concert Hall, with the continuation of the year-old Signature Comedy Series, and one-night-only appearances by Tracy Morgan; Maz Jobrani, founding member of the Axis of Evil Comedy Tour; and YouTube comedy star Miranda Sings.

A new event, the District of Comedy Festival, will be staged June 22-25 in the Concert Hall and Eisenhower and Terrace theaters. This will involve separate shows by Jane Lynch, Dick Gregory, Adam Carolla, Norm Macdonald and Robert Post. In addition, Melissa Rivers will preside over a one-night tribute to her late mother, Joan, featuring a yet-to-be-announced cast of comedians and actors.

Matthew Winer, the center’s director of special programming, said a goal of the events is to provide a diverse sampling of comedy for a broad range of audiences. “In celebrating Joan Rivers, we are paying tribute to one of the comedy greats,” he said, adding that the appearance by Gregory and his “Evening of Comedy and Jazz” harkens back to a time before comedy clubs were the dominant live venue for stand-up. Conversely, the inclusion of a performer of the moment such as Colleen Evans — known to her young fans on the Web as Miranda Sings — amounts to outreach to other audiences the center wants to entice into the complex on the Potomac.

“Her primary demographic is high school girls,” Winer said of Sings. “We don’t do a lot of programming that appeals to that group.”

All of these events may start to address the laughter drought that has persisted over the years, with “Shear Madness” being the institution’s major comedy attraction. (The annual evening celebrating the recipient of the Mark Twain Prize for American Humor is the other prominent entry in the category.) The mindlessly silly interactive murder mystery, which also has run for years in Boston and boasts of having been seen by more than 11 million theatergoers worldwide, survives principally on an audience of tourists and high school groups.

For the Kennedy Center, it is a highly dependable revenue stream, earning the institution about $600,000 a year, money that helps support other programs.

But its de facto permanent presence in what amounts to the nation’s leading home for the performing arts has long been a rather bizarre fact of the city’s artistic life. World-class orchestras and ballet companies come and go from the center’s stages, but the lowbrow “Shear Madness” seems to be forever.

That endless residency has come under review by the administration of Kennedy Center President Deborah F. Rutter. Privately, center officials have spoken of “Shear Madness” vacating the premises entirely, and at one point there was talk of the show leaving the Theater Lab as soon as the end of this year. But in a phone interview on Tuesday, Van Leer indicated that some role for “Shear Madness” was still favored, in what he described as the “mixed economy” the center envisions for the lab’s programming. One possibility that has been discussed, those with knowledge of the talks say, is for “Shear Madness” to rotate into the lab at certain times of the year.

Whatever arrangement is struck, the Kennedy Center, it seems, remains unable to muster the creative resources to replace “Shear Madness” in a financially effective way. “Part of their audience is a tourist audience,” Van Leer said. “And we don’t want to underserve that audience.”