Cate Blanchett as Blanche DuBois in "A Streetcar Named Desire," which appeared at the Kennedy Center in 2009. (Richard A. Lipski/The Washington Post)

Can the Kennedy Center dream bigger?

For an institution striving to be America’s premier showplace for the performing arts, the pressure to be all things to all constituencies has to be enormous. To be a center of both elite cultural endeavor and populist appeal; to provide a balanced, content-rich environment for ballet, opera, modern dance, classical music, jazz and theater; to feed a local as well as a national audience, requires a juggling act of consummate fiscal skill, artistic taste, diplomatic acumen and political timing.

With the appointment Tuesday of a new president — Deborah F. Rutter, chief executive of the Chicago Symphony Orchestra — a vital question comes back into play, not only with regard to how all the pins of the center’s mission will continue to fly, but also, in what new directions they might be propelled. With the intense financial challenges being brought to bear on the arts across the country, this may be as difficult a period as any in memory in which to ask a behemoth of the center’s size and scope to grow its vision.

Still, it must be asked to reach higher. No institution of its stature is meant to nourish its patrons on a diet of low-hanging fruit. I can only reflect on one aspect of the Kennedy Center’s mission, the one that I cover, the theater. And in this sphere, the organization certainly has lots of room for growth, especially if it has designs on an alpha-role in the presentation of the best of an important American art form.

The naming of Rutter to succeed Michael M. Kaiser, who’s been in charge there for more than a decade, bodes well for classical music at the center, which has a huge stake in the maintenance and bolstering of the quality of the National Symphony Orchestra. With so many of the country’s opera companies and orchestras under siege, the search committee’s decision to go with a seasoned steward of a major ensemble is eminently sensible.

The more interesting tests of Rutter’s leadership may come in how she handles producing and scheduling work in disciplines with which she has no managerial experience. Theater may be the most challenging for her of all — at least if she has any ambition to move the needle on the center’s rather anemic dramatic meter. I hope that she considers a strengthening of staffing, alongside the center’s well-liked and knowledgeable theater producer, Max Woodward. Because the center needs to add the voice of an independent-minded tastemaker to shake the place up, force it out of the complacency that seems to consume too much of its theater program.

Theatrically, the Kennedy Center over the past decade has been like some lumbering, dozing giant that occasionally wakes, gets some exercise — and goes back to sleep. Kaiser started strong in 2002 with the Sondheim Celebration, a round-robin revival of six musicals by Stephen Sondheim that showcased a new generation of musical-theater actors and refocused the national spotlight on the genius of the American musical theater’s greatest living composer-lyricist.

No theater event there since has been as significant. Some notable successes have followed, including a marathon series of staged readings of all 10 plays in August Wilson’s 20th Century cycle; appearances by Cate Blanchett in her Sydney Theatre Company’s productions of “A Streetcar Named Desire” and “Uncle Vanya” and Sally Field in “The Glass Menagerie.”

Still in the works is a new version, directed by Bill Condon, of the failed 1997 musical “Side Show” and, in a rare pivot, an original musical by Lynn Ahrens and Stephen Flaherty based on a Edgar Degas sculpture, “Little Dancer.” Other than its family-theater offerings, though, the fare produced by the center has been virtually all in the category of play and musical revivals, some good, some not so good. And the seasons have been filled out with national tours that traverse the spectrum of quality, from wonderful (“The Book of Mormon”) to painful (“Sister Act”).

As a multipurpose institution, in which theater is required to share space with orchestras and dance companies, both home-based and visiting, as well as weeks-long festivals highlighting performing arts around the world, the Kennedy Center is presented with unique booking issues. Not the least of these is a protracted lead time that hinders efforts to stay on top of rapid changes and emerging trends and artists.

At one time, the center’s lack of local competition meant it could get away with some lazy programming. But things in D.C. are changing. By virtue of the relationships it has forged with theater organizations in Britain and elsewhere, the Shakespeare Theatre Company has seized the crown as the region’s best importer of high-end drama, whether via London’s National Theatre (in “Phèdre” with Helen Mirren), the National Theatre of Scotland (“Black Watch”) or New York-based Baryshnikov Productions (currently here with “Man in a Case”).

On the more populist front, the status quo is also being upset, thanks to a new management team that is bringing the National Theatre back from the dead. While the Kennedy Center was giving the keys to the Opera House to the dreary “Sister Act” and preparing for the arrival of other brand-laden commodities like “Elf” and “Flashdance,” the National was hosting the most talked-about big-budget musical of the fall: the pre-Broadway tryout of the original musical “If/Then.” In another sign of a chink in the center’s market dominance, Disney’s Broadway musical “Newsies,” a surprise family hit, recently announced that the venue for its D.C. stop in the spring of 2015 would also be the National.

One hopes Rutter will think deeply and meaningfully about what the Kennedy Center might achieve, in stepping away from some moribund practices and investing more forcefully in new American drama, in using its Theatre Lab as a real theater laboratory, and not just for the endless run of “Shear Madness,” and in seeking out new relationships with major theater companies of the world, much as it has in the realms of dance and classical music. For the real value of her leadership in Washington may not be in what she already knows, but in what she learns.

An earlier version of this story had an incorrect date for the arrival of “Newsies” at the National Theatre.