In the new Yorgos Lanthimos film “Kinds of Kindness,” a character played by Emma Stone recounts a dream in which she was the denizen of a bizarre world. “There, dogs were in charge,” she murmurs. “People were animals, animals were people.” But being brought to heel by their canine masters wasn’t as bad as it sounds, she says: “I must admit, they treated us pretty well.”

Compared with how the human beings treat each other in “Kinds of Kindness,” a dark new comedy that just premiered at the Cannes Film Festival and is in theaters June 21, the dogs would surely be an improvement.

Comprised of three separate stories with the cast members recurring in different roles, “Kinds of Kindness” begins with the tale of Robert (Jesse Plemons), a corporate underling whose every interaction in life — including what to eat, how to speak or even who to marry — is controlled by a boss (Willem Dafoe) whose decisions send poor Robert into a tailspin. The second story follows Daniel (Plemons again), who becomes convinced that his wife (Stone) is not who she claims to be and coaxes her into insane tasks to prove herself.

And in the third sequence, cult members played by Stone and Plemons search for a woman able to wake the dead, though the whims of their guru (Dafoe) dictate that this mysterious woman also be a certain height and weight and have an identical twin. (Even when it comes to awesome supernatural powers, there are dealbreakers.)

On Saturday afternoon in a hotel here in Cannes, I met with Stone, Plemons and Dafoe to try to make sense of this triptych. According to the actors, Lanthimos isn’t keen to give too much away. “Yorgos says he likes it when people have different takes on the movie,” Dafoe said. “I think that’s the strength of it.”