The first thing you’ll likely notice about His Three Daughters is the way the characters talk. Framed against a white wall in her father’s (Jay O. Sanders) Lower East Side apartment, an arms-crossed Katie (Carrie Coon) insists that she and her sisters set any differences aside, even as she begins to grumble about the “do not resuscitate” order that Rachel (Natasha Lyonne) didn’t get signed. It’s a capital-m monologue that Coon delivers in a breathless and stilted cadence, leaving no room for Rachel to speak. By the time Christina (Elizabeth Olsen), the youngest of the sisters, hunkers down at the dinner table for her turn in the spotlight, you may be excused for thinking you’re watching a theater group putting their spin on a relay race.

The stagey quality makes a certain amount of sense for writer-director Azazel Jacobs’s film. After all, Katie and...