“Please Give” opens with a shot of a naked female breast casually resting on a mammogram table as if it were a pillow. “I don’t see them as breasts. I see them as tubes of potential danger,” a character quips, deadpan.

This image is followed by another breast, and then another. Down they pass before our eyes, as if they were on an assembly line – small, large, fat, crooked, sagging, discolored – a profoundly jarring scene that aptly sets the tone for the rest of the film.

Director Nicole Holofcener (“Friends With Money”) saturates “Please Give” with an interior depression that doesn’t hit right away, what with the cheerful shots of vintage furniture and artsy Manhattan walkways. Yet there’s a bitter core behind all the barbed wit and pseudo-intellectual posturing. Although its heroines possess enough New Yorker neuroses to fill up a Woody Allen film, “Please Give” features an array of brittle, hard-edged ladies with emotional sores as painful as the zits pustulating on teenager Abby’s face.

Leading the pack is Kate, played by indie darling Catherine Keener (“Where the Wild Things Are”), who owns a trendy vintage furniture shop together with her husband Alex (Oliver Platt, “2012”). With macabre insensitivity they wait for their elderly neighbor Andra to die so that they can knock down the walls to expand their apartment, and probe the obituaries for the recently deceased so they can snatch their old furniture up like magpies. Wracked by guilt by their callous display of selfishness, Kate tries to make up for it by donating hundreds of dollars to the homeless on the streets.

Then there’s Rebecca (Rebecca Hall, “Frost/Nixon”) and Mary (Amanda Peet, “Something’s Gotta Give”), Andra’s two granddaughters. Rebecca is tall, ungainly and shy, constantly trying to do the right thing but always getting the worse end of the deal. Mary is self-absorbed, overly tanned, relentlessly honest and insecure, involving herself in an emotionless affair with Alex for reasons she can’t quite make out.

And last, there’s Andra herself (Ann Morgan Guilbert, TV’s “The Nanny”), desperately trying to claw her way out of her impending grave through any means possible. The brunt of the humor of this sharp-edged satire lies with Andra’s caustic senility, as one particular scene watches Andra decisively throwing Kate and Alex’s well-meaning birthday gift of lotions and body products straight into the trash chute.

It all reads like a particularly black-humored situation comedy, but Holofcener imbues her heroines with such realism and sting, the humor tends to hit too close to home. These characters are funny, but their neuroses cut so deep that they no longer resemble caricature. The result is a startlingly potent picture of women and the emotional baggage that they carry with them.

Towards the end, all the characters’ issues remain unresolved, with each woman in approximately the same place as when she started off. Holofcener has proved her ability to create solid portraits of women in her last three films, but this time it just leaves us wanting more. Whatever that might be – reconciliation, maturation or comeuppance – there’s something ultimately unsettling about a film that offers no resolution. But maybe that’s the point.