Watched without sound, the Broadway production of Mike Bartlett’s KING CHARLES III would suggest a Shakespeare in modern dress, a tragedy or a history, drawing some sort of parallel with the current royal family. Maybe it’s Henry IV: there’s a fellow who looks like Harry cavorting with commoners. And the guy who resembles Charles (a woman who must  be Camilla tags about with him) – is that Hal’s dad? Who’s that young man who looks like William? And the woman with gestures very like Kate’s? How do they fit the Henry plays? Hotspur and his Kate? Ah, the ghost of a woman, her hair styled like Diana’s, crosses the stage – Richard III?  Someone looks to be hearing cries in the night. Macbeth? Julius Caesar?  But where are the witches, daggers, blood and yawning graves? One of the comedies, maybe?

Not on your life, although there’s comedy to be had in the cleverness of it all. Turn up the sound and KING CHARLES III is still a lot like, without ever pretending to be, Shakespeare. The dialogue is amusingly versified, punctuated by soliloquy, the action is continuous, there’s a lowlife subplot; Rupert Goold’s direction and Tom Scott’s design are textbook Elizabethan. It’s a “future history play” of the coming reign of Charles III, after Elizabeth II has passed, and takes with the future no more license than Shakespeare took with the past – perhaps less, for it is too soon to know! The personalities behave about as we expect: Charles with a greater urge to influence policy than his mother, Harry with rebellious resentment at his lot (but not his privilege), William with dutiful correctness, Kate and Camilla wielding hidden power in a re-masculinized court (not to mention, as Kate avers in a sly soliloquy, the hard-to-tell-apart prime minister and opposition leader, both men). This is great fun, as satire and pastiche, but there is something serious in it too, humanly and politically.

KING CHARLES III is steeped in historical knowledge, particularly of the century after James I, when conflicts over parliamentary rule and royal prerogative caused the head of the first Charles to be chopped off, restored the second Charles after Cromwell’s brief (and repressive) protectorate, and redefined English governance in the Glorious Revolution and its upshot. CHARLES III can be seen as cautionary tale of monarchial overreach or affirmation of it as the ultimate stopgap. What if the next monarch exercised prerogatives that have, in the modern era, been conventionally, but not by law, restrained? In Bartlett’s scenario, the third Charles begins his reign by declining to sign an act of parliament that restricts the freedom of the press. This is an ingenious device, dramatically, in that it puts the inclinations of a liberally minded viewer, or, for that matter, a conservative one, at odds. Add the human drama of a ruler who wants being royal to mean something, beyond the pretty symbolism of a William and Kate, or the late Diana, and you have the intersection of the personal with the historical that gave Shakespeare’s chronicles significance and emotional power.

KING CHARLES III turns people who are going to be historical figures into fictional past-tense characters. Tim Pigott-Smith looks, in some way hard to pinpoint, a lot like Charles, although he wouldn’t be mistaken for him in life (he lacks the cartoonishly narrow face). He acts a lot like him too, in voice and manner, but doesn’t impersonate him, any more than he would one of Shakespeare’s original kings. Pigott-Smith takes Charles seriously and sympathetically, as a person with his own mind, with values that aren’t constrainable by ceremony, a king out of time with a calling that custom no longer permits. He precipitates a crisis, and brings on a solution that feels tragically unsatisfactory; the empathy it arouses comes from thinking of ways he might have asserted himself more shrewdly. Oliver Chris and Richard Goulding are more spitting image as his sons than he is of Charles. Chris verges on twinship with the real William, and Goulding is especially spirited as Harry, perhaps because his commoner love interest, Jess, is so infectiously played by Tafline Steen. Lydia Wilson, as Kate, bears less physical resemblance than the others, but she’s got down the style and the rehearsed gestures. It is given to her to articulate the court’s backstage feminism (practiced in rivalry with Margot Liecester’s spot-on Camilla) in the best of Bartlett’s soliloquies, which, as she delivers it, is deliciously savvy.

However the real succession pans out, KING CHARLES III ought to endure. It makes a nod at most of the scenarios that have been speculated on. Perhaps it will be seen as prescient, or, if things turn out in a markedly different way, as an alternative history, a “what if” rather than an “as is.” Either way, it is deeply pleasurable for now, and at the same time substantial, a template for thinking about power and privilege in general; the prerogatives of birth aren’t limited to royal families and wisdom isn’t passed out just to those at the bottom. The case for or against monarchy in a democratic society doesn’t seem so clear cut in the end, but that history will always intersect with real human feeling does.

 The Almeida Theatre production of KING CHARLES III ran through Jan. 31 at the Music Box Theatre.