Alessandra Baldacchino as “Small Alison” and Robert Petkoff as “Bruce” in “Fun Home. (Joan Marcus)

In the coming months, many eyes will be looking with hopes raised to the new tenant on Pennsylvania Avenue.

I’m referring, of course, to “Fun Home.”

The musical by Jeanine Tesori and Lisa Kron, which collected five Tony Awards in 2015, including best musical, settles into Washington this spring at the National Theatre, just a few blocks down Pennsylvania from the White House. In a theater season packed with promising ventures, this one, running from April 18 to May 13, should find a slot high on your priority list.

The august National, once an essential stop for important shows on their way to and from Broadway, only rarely plays that role anymore. The last time was almost four years ago, when it housed the pre-Broadway tryout of Tom Kitt and Brian Yorkey’s “If/Then,” starring Idina Menzel. Although touring shows still cycle through the building, “Fun Home” is a musical of a rarer level of distinction. In both style and content, it accomplishes that in­cred­ibly formidable task: launching a piece of musical theater off toward new, imaginative horizons.

Based on a graphic memoir by MacArthur “genius grant” winner Alison Bechdel, it is a funny and disturbing account of growing up gay in a family that runs a funeral home — thus the title. Alison, played at various ages by three actresses, not only must come to terms with her identity, but must also contend with the secrets in her family — most notably, a deeply unhappy father who is himself a closeted gay man. (For the road company of “Fun Home,” directed as in New York by Sam Gold, Kate Shindle plays the adult Alison; Robert Petkoff portrays her father, Bruce; and Susan Moniz, her mother, Helen.)

The material, deeply personal and tinged with sadness, is nevertheless made buoyant by Kron and Tesori’s heartbreaking score, filled with vivacious, coming-of-age melodies and more plaintive ballads of self-revelation. It’s a musical of surprising richness, the kind that envelops you in its glowing compassion and knowing humor.

Also worth noting
The regional debut of Mike Bartlett’s award-winning play explores what England would be like if Prince Charles became king. (Courtesy of Shakespeare Theatre)

Fascinating twists on established forms also characterize the coming months’ noteworthy plays. One of these is the newfangled cheekiness that suffuses playwright Mike Bartlett’s “King Charles III,” which begins at Shakespeare Theatre Company on Feb. 7. This fantasia of a play, directed by Studio Theatre’s David Muse, stars Robert Joy as the newly crowned successor to a recently deceased Queen Elizabeth II. And it asks some pointed questions about the relevance of a monarchy at this late date.

A classical theater company is the best possible host for this play, which got something of a puzzled response from Broadway theatergoers. Modeled on Shakespeare’s history plays — and spoken, yes, in Elizabethan-era meter — “King Charles III” is the sort of bracingly intellectual entertainment best enjoyed by those with some experience of, say, “Richard II” or “Henry V.” The ways in which Bartlett uses the conventions of Shakespeare are just that sharp. And with its satirical portraits of contemporary royals (even the late Princess Diana makes a spectral appearance), there is enough juicy intrigue to keep any die-hard Windsor-watcher glued to their seat.

At Studio Theatre, the spring brings an even more daring gambit. A revival of Anton Chekhov’s peerless “Three Sisters” is being paired with a world-premiere play by Aaron Posner that dances, in meta-theatrically Stoppardian fashion, with the classics. “No Sisters” is its title, and the conceit — at least on paper — sounds coolly of the moment. Although “Three Sisters,” directed by Jackson Gay, begins performances a week earlier, the two works will run concurrently once “No Sisters” opens March 16.

“Three Sisters” will be performed in the ground-floor Mead Theatre and “No Sisters,” directed by Posner himself, a floor above in the Milton Theatre. Seven of the supporting characters in “Three Sisters” will use a concealed stairway between the two spaces to exit “Three Sisters” and enter “No Sisters.”

It seems silly to see one and not the other, but Posner is no novice when it comes to Chekhov riffs. His previous adaptations of “Uncle Vanya” and, especially, “The Seagull” have drawn positive, even admiring receptions. If “No Sisters” can successfully expose new layers of regret and longing in a theatrical realm we’ve come to know as Chekhovian, that world might henceforth have to be referred to as Posnerian, too.