We meet Steven (Peter Dinklage) while he’s threading his way uneasily through a swank New York music-world gala; a composer himself, Steven is trying to avoid a patron who is considering him for a commission. Shy, neurotic, unable to make eye contact, Steven needs a facilitator, which is where his wife, Patricia (Anne Hathaway), comes in. As Steven’s former therapist — he still calls her “Doc” — Pat has taken caretaking to hyper-controlling extremes, doling out life-skills advice with the same measured evenhandedness as she doles out his fish oil pills. Pat’s a compulsive cleaner — she’s always polishing something in the couple’s immaculate Brooklyn brownstone — but her mania is less about germaphobia than a gaze toward the infinite. Steven is looking for transcendence in the just-right harmonic resolution; his wife finds it in a Windex bottle.

Pat’s the kind of person most filmmakers would turn into a shrew, or shallow self-deceiver. But Miller casts a generous, sympathetic eye on all of her characters, who throughout “She Came to Me” intersect with balletic, if not always believable, bursts of grace. While Steven suffers yet another crippling creative block and Pat scrubs down an already pristine kitchen, Miller shifts the action to a seemingly unrelated, less prosperous family: Trey (Brian d’Arcy James), a court reporter and weekend Civil War reenactor; his partner, Magdalena (Joanna Kulig); and their teenage daughter Tereza (Harlow Jane), a bubbly high school student who has embarked on her first love affair with 18-year-old Julian (Evan A. Ellison).

These two clans eventually come together by way of Miller’s plotty machinations, which also include a chance encounter between Steven and a free-spirited tugboat captain named Katrina, played by Marisa Tomei in an earthy, laconically amusing performance. As a comedy of urban manners and moral quandaries, “She Came to Me” is the kind of fanciful but sophisticated fairy tale reminiscent of Woody Allen in his early years. Its mordant humor also evokes the charms of Miller’s delightfully observant 2015 romantic comedy “Maggie’s Plan.”

Miller sets out an ambitious agenda with “She Came to Me”: In addition to constructing a carefully assembled Jenga tower of comedy, pathos and melodrama, Miller stages a number of opera performances. (The music is written by the National’s Bryce Dessner.) Add a dizzying array of narrative convolutions, coincidences and contrivances and the movie becomes a lot to carry, especially when the tone is supposed to be feather-light. Inevitably, “She Came to Me” can’t help but falter under Miller’s heavy-handed conceits. But when it works, it hums along with irresistible sweetness and eccentricity. The proceedings are kept aloft by a capable, thoroughly committed cast: As Steven, Dinklage brings his signature brand of wounded vulnerability to a role that would otherwise be mired in grumpy passivity; Hathaway lends wellsprings of emotion to Pat, saving a perfunctory arc from becoming a mere punchline.

Then there’s Tomei, the anarchic, sensuous presence whose Katrina blows through “She Came to Me” like the eponymous hurricane. Even at its most overworked and effortful, Miller’s film exudes a lit-from-within kind of joy, much of it emanating from Tomei’s flawed and funny head case. There’s something to be said for in-between-ness, in all its messy glory. It’s where most of us live, after all.

R. At Regal’s Majestic and the Cinema Arts Theatre. Contains some coarse language. 102 minutes.