I’m honestly not sure what Sam Shepard is up to with “Heartless,” his new play at Signature Theatre. It is visually arresting, beautifully directed by Daniel Aukin, and well-acted by a company of five. The quotations from Vladimir Nabokov and Eugene Ionesco that head the script suggest a pervasive existential angst. “Heartless,” however, lacks a sufficiently rigorous internal logic that would allow Shepard to communicate his ideas and emotions in a way that makes them palpable.

There’s no story, really, just a situation. Aging academic Roscoe, a Cervantes scholar, has left his wife and family and followed the much younger Sally home. Little more than a passing distraction to him, she wants a love affair. Sally’s harridan of a mother, Mable Murphy, is confined to a wheelchair after falling out of a pine tree many years before, when her husband also deserted his wife and family. She terrorizes Sally’s older sister, Lucy, her primary caregiver, and her abused around-the-clock nurse, Elizabeth. When she turns her guns on Roscoe, everybody starts to crack apart.

Mable Murphy is the play’s most compelling personage, and Lois Smith commands attention in the part, making hay out of lines such as “I’d like to gaze into the abyss for a while,” which in this case is the San Fernando Valley. The veteran Shepard actor is frightening, fascinating, and grotesquely vulgar as Mable Murphy rules her roost. Smith is riveting in a climactic Act 1 speech in which we learn why Sally has an angry red scar running the length of her torso, the result of a heart transplant she received at age 10.

Julianne Nicholson’s bitter, waspish Sally retains an intriguing girlishness. When Sally sings a simple a cappella ditty, “I Want to Stay Alive,” Nicholson makes it a difficult act of self-persuasion. Jenny Bacon’s sullen, put-upon Lucy grows increasingly outrageous as the evening wears on, providing some welcome black humor. Betty Gilpin’s Elizabeth at first is mute, and Gilpin is a forceful concentration of barely contained suppression. She’s also impressive in a long slow-motion scream that marks the character’s transition to speech. Roscoe plays the straight man to the heightened women surrounding him, and Gary Cole’s shaggy self-absorption and manufactured niceness are just right.

Eugene Lee’s simple set of battered patio furniture, two single beds, a couple of palm trees, and a steeply raked upstage wooden platform beyond which yawns emptiness makes good use of levels and facilitates Aukin’s sculptured staging. Tyler Micoleau’s careful lighting carves out space well, Kaye Voyce’s contemporary costumes are subtly stylized, and Eric Shimelonis’ sound reinforces the production’s sense of hovering doom.

It’s clear that Signature Theatre has given much loving attention to “Heartless.” Nevertheless, despite containing some striking set pieces, this airless symbolic drama fails to accrete in a persuasive way.