A dying father brings 'His Three Daughters' together, in a sharply written film

Over the years I’ve seen more than my share of dysfunctional-family movies and terminal-illness movies, and even the good ones have trouble sidestepping clichés. So it says something that His Three Daughters, which is about a dysfunctional family coping with a terminal illness, doesn’t feel like a retread.

The writer-director Azazel Jacobs has a knack for putting a fresh, intelligent spin on familiar material, from the high-school misfit comedy Terri to the playful marital drama The Lovers. His latest, His Three Daughters, is a sharply written and beautifully modulated chamber piece, set over a few days inside a Lower Manhattan apartment where three women have gathered to bid farewell to their father, Vincent, who’s in hospice care.

Carrie Coon plays Katie, the oldest of the three sisters. She lives in Brooklyn with her husband and teenage daughter, but she hasn’t been around to visit her dad much lately. Elizabeth Olsen plays the youngest, Christina, who’s flown in from her home thousands of miles away.

And then there’s Rachel — that’s Natasha Lyonne. She lives with Vincent in this apartment and has been looking after him for some time. Rachel is estranged from her two sisters, for reasons that aren’t initially clear. Jacobs drops us right into the thick of the tension, then gradually fills in the larger picture.

Some of the friction stems from the fact that Katie and Christina are essentially outsiders on Rachel’s turf. Rachel can claim some moral high ground, since she’s been taking care of their dad while they’ve been busy living their lives and raising families of their own.

Adding to the two-against-one dynamic is the fact that Rachel isn’t biologically related to her sisters or their father. After Vincent’s first wife died, he married Rachel’s mom and raised Rachel as his own. As Rachel makes needlessly clear to her sisters, she’s no less his daughter than they are.

There are money and class issues, too; Katie looks down on Rachel, claiming all she does is smoke weed all day and make money through sports gambling. And then there’s the matter of real estate. In one contentious conversation, Katie insinuates that Rachel has been taking care of Vincent partly because of her enviable living situation.

In this and every other scene, the acting and the writing have such specificity that you feel you know these characters intimately. Few actors can make anger more mesmerizing than Coon, and her Katie is testy and judgmental, even — or especially — when she tries to seem reasonable.

It’s hard not to side a lot of the time with Lyonne’s Rachel, who lets the expletives fly as she pushes back defensively against Katie’s insinuations. That leaves Christina in the tough role of peacemaker. She’s earnest and open-hearted by nature, something that comes out when she describes her Deadhead past. In Olsen’s quietly moving performance, we see a woman who often suppresses her feelings to spare those of others.

What distinguishes His Three Daughters from so many movies of its type is that while it’s certainly talky, it never feels as if the characters are trying to explain themselves to you. Rather than coughing up large chunks of backstory, their interactions have the pull of honest, free-flowing conversation.

Much of the dialogue is taken up with the practical and wholly relatable end-of-life details: the difficulties of writing an obituary, or arranging a do-not-resuscitate order, or even dealing with a well-meaning but slightly exasperating hospice care worker. I haven’t seen many movies that so acutely understand the role food plays in a situation like this, where the act of cooking meals for your family or making sure there’s always fresh coffee can be both a drag and a welcome distraction.

Vincent himself is off-camera for most of the movie, sleeping quietly in his room, though Jacobs wisely gives him — and Jay O. Sanders, the actor playing him — a beautiful moment in the film’s last act.

The question hanging over His Three Daughters is whether the sisters will overcome their estrangement and remain family after Vincent’s gone. Jacobs doesn’t force a resolution, though he does end on a note of hard-won understanding that I found both optimistic and deeply affecting. He’s made a movie that, in the shadow of death, says something essential about how we live.