If you had to choose a dog breed to tie together themes of mortality, disease, depression and thwarted ambition, it’s unlikely that the first to come to mind would be a smooth-haired dachshund. Chipper little hounds, with an inherently comic waddle, they are too upbeat to fit neatly into this portmanteau picture with its overriding theme of disappointment. And yet director Todd Solondz’s gift for casting clearly extends to animals. The two dogs that combine to play the single central role manage to display exactly the tone of nervy, neurotic uncertainty that you would expect from the lead in a Solondz movie. It’s something about the expressive anxious droop of the ears, combined with a gift for physical comedy that is a birthright if your legs are barely an inch or two long. This hapless canine serves to highlight the failings of the humans around it.

Solondz cites as disparate influences Au Hasard Balthazar, Robert Bresson’s tale of a long-suffering donkey, and Benji, the tale of a plucky mutt who rescues two kidnapped kids. In its episodic structure, if not in tone, the picture also has something in common with War Horse – human lives are touched, albeit briefly, by a noble animal, although Solondz’s approach is decidedly heavier on irony than that of Spielberg.

The dog, renamed by each new owner, is the link between the four chapters in the picture. Her first human companion is Remi (Keaton Nigel Cook), a young boy who is recovering from cancer. His father, Danny (Tracy Letts, full of rage and hard edges), bought the dog on a whim. It’s yet anothe r source of conflict between Danny and his wife, Dina (Julie Delpy), in a house that feels like an immaculately furnished war zone. The famous Solondz attention to detail is in evidence in the production design here. This is a home that screams control. Clean, cold surfaces, sharp angles; the way Delpy grimly disembowels the bread she is bullying into a sandwich while Letts spits his words as he deconstructs the concept of “house-breaking” (house-training, as we say in Britain).

Ultimately, it’s the house-breaking, or lack thereof, that proves the undoing of the dog. Debussy’s Clair de lune is one of the most overused pieces of music in cinema, but it’s safe to say it has never before been employed to accompany a tracking shot that takes in the devastating aftermath of a dog’s gastric emergency.

The second chapter in the dog’s life comes when she is granted a reprieve from a death sentence and nursed back to health by vet’s assistant Dawn Wiener (Greta Gerwig). Audiences first met Dawn, then played by Heather Matarazzo, in Solondz’s 1995 film Welcome to the Dollhouse. As with Life During Wartime (2009), which loosely revisits but recasts the characters from Happiness (1998), Solondz allows the new actors creative leeway in their interpretation of the original roles. But although Gerwig brings an awkward, needy charm to her portrayal of Dawn, there’s not much, apart from the unflattering glasses, that links her to the younger version of the character.

Dawn, we gather from her choice of shapeless, washed-out clothes and colourless demeanour, has been going through a rough patch. The dog, whom she rechristens Doody, makes her feel needed, makes her feel alive. And when after a chance meeting with her school boyfriend/bully Brandon (Kieran Culkin takes over the role from Brendan Sexton III) he invites her to come on a road trip, she accepts. Despite, or perhaps because of the quality of Gerwig’s performance, this is the least satisfying chapter of the film. We are not quite ready to leave Dawn when the film does, when the dog is donated to Brandon’s brother, who has Down’s syndrome, to help him get over a tragic piece of news.

Following a cute but slightly redundant intermission sequence, the story continues. The dog is now in the care of a film lecturer and former screenwriter called Dave Schmerz (Danny DeVito). Solondz approaches each story with his distinctive blend of cruelty and compassion, but there’s an added layer of bitterness here that suggests a personal investment in his particular strand. Schmerz takes each student’s screenplay as a personal slight; every success that isn’t his own is salt in the open wound of his failing career. When he finally snaps, his dog is the visual punchline used to vent his frustration on all who fail to recognise his talent.

The dog, now renamed Cancer (“It felt right,” snarls the new owner, played by Ellen Burstyn), ends up as the companion of an elderly woman and plays a peripheral role in one of the most savagely effective scenes in the film. Granddaughter Zoe (Zosia Mamet) comes to visit her nana after a long absence. The unloved trinkets amassed over a lifetime sit in silent judgment, as Zoe stumbles through her repertoire of small talk until she finally gets to the point of asking for money. However great Burstyn is, it’s Mamet who registers here as the dynamic force on the screen. She’s flat-out terrific, and the most memorable element of a film that never quite matches the clarity of approach achieved by the similarly structured Wild Tales.