Cat on a Hot Tin Goof: Williams and the American play a little bluff.

A remote locale, an esoteric menu, urbane conversations, various supernatural goings-on: Kathleen Akerley’s new play Theories of the Sun, a mournful valentine to storytelling and the stage (and more besides), may seem a trifle overstuffed—especially to anyone who insists on ticking the “Ooh, I get it” box next to each literary reference and every theatrical homage.

Tom Stoppard and Tennessee Williams, you see, are both supporting characters—which itself is a little love note to Stoppard’s Travesties—and Akerley, one of D.C.’s most unapologetically thinky theatermakers, buries highbrow Easter eggs like a code geek working on a flashy new iPhone app.

Rosencrantz & Guildenstern coin-flip? Check. Purple monologue suggesting ­Williams-esque mysteries of womanhood and death? Check. Zeno’s paradox name-check? Er, check. And that’s without going into the macro issues—how the play’s hothouse, hoodoo-haunted dalliances with place and time and character seem to suggest everything from Rosencrantz and Arcadia to Camino Real and The Milk Train Doesn’t Stop Here Anymore.

But let that catch-the-reference impulse go, and you might find that Theories of the Sun works nicely enough on its own terms, as a metaphysical yarn: A mother, a daughter, a man (or three), and a mystery (or two) are what it’s really about. That, and our perpetual drift in the direction of mortality, and the sadnesses and joys we trail in our slow wake.

The Sweenys, mother and daughter, arrive at a secluded French hotel run by proprietor (Daniel Vito Siefring) with a supernatural knack for knowing where and when to turn up. The date: 1963. The other guests: Williams (Michael Glenn), who’ll be revealed later to be mourning the death of his longtime love, Frank Merlo; Stoppard (the grandiosely named Dylan Pinter), who’s trying to wrap his head around the concept that will soon become Rosencrantz and Guildenstern Are Dead; a local doctor (Jason Lott) with a near-impenetrable accent, who’ll turn out to have some of the answers the ladies have come in search of; and a nattily dressed American (Jason Stiles) with a knowing look and bag tags that suggest he’s used more than one name recently. (Watch that last one: He’ll prove important, though even now I’m not sure I can tell you precisely why.)

And one figure more—Michael John Casey’s admirably contained Mr. Asher, who introduces himself as a scholar of old-world sun mythologies—haunts the lyrical blue evenings, launching what looks like a flirtation with Abby Wood’s Elizabeth Sweeny, a fresh-faced beauty with the poise and the reserve of a much older woman.

She’s dubious, so he lulls her with the tales he’s scavenged from the civilizations of several millennia: a hunter who climbs the face of the sky, chasing a superb music, only to burst into flame; a hive of infinite suns that sends a blazing one across our sky each day, never to return to its home; a mourning woman who encounters the source of all things, inspiring it to light the sky for her.

These exquisite creation stories are the spine of the play, the structure that supports the plot’s other mysteries, and Casey delivers them with such grace and gravity that you may have to remind yourself they’re Akerley’s inventions; they have the heft of stories distilled by generations of griots, and the mind-pictures they create are marvelous.

Would that the same could be said for everything that transpires in the three-hour span of Theories of the Sun. It’s by no means certain, for example, that the (admittedly amusing) business about the asparagus and the urine samples pays off sufficiently to warrant the time it consumes. And while the evening’s central thread—involving the answer to the Sweenys’ medical mystery, and the real story behind Mr. Asher’s lovely stories—unspools itself nicely enough, there’s still that stubbornly knotty end of it involving the mysterious American, whose motivations (to say nothing of his abilities) will need someone cleverer than I to decode them.

Yet the “what” of that conclusion, for all the mild confusions attached to its “how,” feels right and inevitable and sad. Akerley’s Barbara Sweeny, left to sort things out, is every survivor who’s ever asked why, every parent or partner or child who’s ever hoped that it was quick, that it didn’t hurt, that there wasn’t too much horror involved. And the men who remain offer explanations, each filtered through the lens of his own understanding of what has just been, each one only partly comprehensible to Barbara—who as the person closest to the loss can understand it least, even as it looks her frankly in the face.