By Michael Schulman

The theatre has the power—more like the prerogative—to warp reality to suit its own ends, exiting the literal world through whatever trapdoors it creates. Why does an angel crash through a gay man’s ceiling in “Angels in America” and declare him a prophet? Because Tony Kushner said so. In screenwriting, there’s always talk of the “rules”: the time machine only works at eighty-eight miles per hour, etc. Onstage, suspension of disbelief works by more poetic guidelines, as long as playwrights have the wit and conviction to dream them up.

Two current productions—one on Broadway, one Off—depict powerful people in fantastical ways that, paradoxically, reach them at their core. In “King Charles III,” at the Music Box, the dramatis personae include Kate Middleton, Camilla Parker Bowles, and Princes William and Harry. In “First Daughter Suite,” at the Public, the characters are Betty Ford, Laura Bush, Amy Carter, and Nancy Reagan, to name a few. There’s a humorous thrill in seeing these people represented onstage, especially, as in “King Charles III,” when the actors look strikingly similar to the real ones, right down to the hairstyles. (Would it really be Kate Middleton without those bouncy brown curls?)

The strength of both shows, though, isn’t verisimilitude but invention. The fantastical and absurd can sometimes yield more insight than realism. Helen Mirren nailed her role as Queen Elizabeth II last season, in Peter Morgan’s “The Audience,” which imagined her meetings with various Prime Ministers over the decades. But Mike Bartlett’s “King Charles III” imagines something more exotic: the future. When the action begins, Queen Elizabeth II has died, and her son, Charles (the excellent Tim Pigott-Smith), is expected to ascend to the throne—finally. It’s not clear how far in the future this is, but it’s not much: Charles is gray-haired but not elderly, William (Oliver Chris) and Kate (Lydia Wilson) are parents of two small children, and Harry (Richard Goulding) is a rascally thirtysomething who sneaks out to meet girls at clubs.

Given the plodding inevitability of the British line of succession, it’s exciting, even for an American audience (let’s face it, we’re royally obsessed), to fast-forward to the next big turn of the wheel. To the expected pomp and circumstance, Bartlett adds dashes of trouble: a crisis in Parliament forces Charles to rethink his ceremonial role, while Harry takes up with a spunky alt chick who believes the Royal Family is a scam perpetrated on the taxpayers. But what makes Bartlett’s script so mesmerizing is less its plot than its language—he has written the play in blank verse, like counterfeit Shakespeare. Says Charles:

            Sometimes I must confess I ’magined if

            My mother hap’ed to die before her time,

            A helicopter crash, a rare disease

            So at an early age I’d be in charge—

            Before me years of constant stable rule.

The ear quickly adjusts to the modern-day iambic pentameter (we’ve been trained by all those productions of “Macbeth” set in the post-apocalypse, or wherever), which gives the proceedings a larger-than-life heft: we realize that, however trivial we may find the royals, we’re witnessing “history,” in which personal choices have national consequences. It’s the same quality you’d find in a good production of “Henry V”—or, if not quite as weighty, we’re reminded what little power English monarchs wield these days: a newfangled mock-epic. Echoes of Shakespeare weave through the story: Diana haunts Charles, like the ghost of King Hamlet, and Prince Harry starts to resemble Prince Hal, right down to the final betrayal. Even Kate Middleton, it turns out, has shades of Lady Macbeth—who knew?

Rendered on screen or even in prose, all this might have felt like a fan-fic edition of the Daily Mail. But, liberated from conventional speech and historical fact, Bartlett pushes his characters to extremes he wouldn’t have accessed otherwise—the implausible illuminates the plausible. A similar principle applies to “First Daughter Suite,” by the composer and lyricist Michael John LaChiusa. In his psychological nuance and experimental sound, LaChiusa is part of the generation heavily marked by the influence of Sondheim, which doesn’t mean that he can’t be any fun. In 1993, LaChiusa wrote “First Lady Suite,” which covered Eleanor Roosevelt, Mamie Eisenhower, Bess Truman, and Jacqueline Kennedy. “First Daughter Suite” is a follow-up, purportedly about the lives of Presidential daughters. But it should have just been called “First Lady Suite, Part 2”—in all four of its vignettes, the First Ladies are the far more compelling characters, with the daughters serving mostly as catalysts.

The first segment opens on Pat Nixon (the formidable Barbara Walsh), in a sitting room of the White House. It’s her daughter Tricia’s wedding day, but the weather is iffy, and the bride (Betsy Morgan) is squabbling with her sister, Julie (Caissie Levy). But mostly we’re interested in Pat, who keeps a wary eye on her husband’s machinations. (We’re on the cusp of the Pentagon Papers fiasco.) Anticipating her role weathering her husband’s self-inflicted downfall, she sings:

            Take his hand.

            Don’t let him surrender,

            Hard as it seems.

            And shoulder through the flames of your burning, dying dreams.

All well and good, but what really sold me on “First Daughter Suite” was the second vignette, titled “Amy Carter’s Fabulous Dream Adventure.” We are, indeed, inside the dreaming mind of Amy Carter, age twelve, on the deck of the Presidential yacht. In her fantasy, she has conjured not just her mother, Rosalynn (Rachel Bay Jones), but Betty Ford (Alison Fraser) and Susan Ford (Morgan again). Amy idolizes Susan, a cool girl in aviator sunglasses, but it’s Fraser’s Betty Ford, rendered as a dippy, fun-loving drunk, who steals the show. The scene takes several ridiculous turns, including a side trip to Iran and Rosalynn Carter quacking like a duck. It all makes a loopy sort of sense—or doesn’t—and frees up the show in a way that Pat Nixon’s quiet fortitude did not. Like Tina Fey’s Sarah Palin, Fraser’s Betty Ford is so nutty and wonderful that she seems realer to us than any History Channel portrait could allow.

The last two segments wed the fruitcake fantasy of the Carter scene with the emotional groundedness of the Nixon scene. Fraser returns, in fine form, as Nancy Reagan, lounging poolside in California as her rebellious daughter, Patti Davis (Levy), hurls invective. The music thrums and crashes along with Patti’s rages, but Nancy doesn’t crack. Instead, a bizarre twist reveals her to be an ice-cold manipulator, not unlike the Kate Middleton of “King Charles III.” Finally, we visit the elder Barbara Bush (Mary Testa) at the family compound in Kennebunkport, bemoaning how her husband’s legacy has been “obscured by a mediocre son” (W., not Jeb). Barbara contends with two daughters: the specter of Robin (Theresa McCarthy), who died of childhood leukemia, and her daughter-in-law Laura (Jones), who pleads with Barbara to go easy on her son.

We all know Barbara Bush’s starchy persona—her clucking pronouncements are still making news—but the fact is that no public figure reveals everything, even in gaffes (and certainly not in memoirs). Shakespeare, in his history plays, gave us a blueprint for how to fill in the blanks, and, as long as there are flesh-and-blood occupants of the White House and of Buckingham Palace, we’ll have speculative work to do. Both Bartlett and LaChiusa have found counterintuitive wormholes into the minds of the powerful: in song, in verse, in the future, and in dreams. Fantasy, in some sense, is where these folks have to live, because their lives are no longer delineated by day-to-day existence. Each has a shadow life in the public’s imagination, which owns some essential part of who they are. That’s where theatre artists in particular can get at figurative truths, catching the conscience of kings by harnessing the unconscious freedoms of the stage.