It’s not Fellini’s “8½,” or even the Broadway musical based on it that twice won Tonys, first in its original 1982 production with Raul Julia and then in its 2003 revival with Antonio Banderas. Rob Marshall’s adaptation of “Nine” is instead a film that takes elements of both, to which it adds its own peculiar approach, and the result is part homage, part recreation, part innovation—but, happily, mostly engaging. Though the combination might not completely gel and there are occasional lapses, it satisfies overall.

Fellini’s film, of course, is one of the touchstones of cinema, routinely cited among the greatest of all time. It’s highly personal and idiosyncratic, an extravagantly surrealistic take on filmmaker’s block and tortured memory, especially over the many women in his life. In translating it to the musical stage, librettist Arthur Kopit and composer Maury Yeston couldn’t hope to duplicate that unique vision, and they really didn’t try. Instead they retained the basic premise and fashioned a highly stylized musical around it, in which the director, Guido Contini, tries to use recollections of women he’s known—including his wife and current mistress, as well as his favorite star—as the basis for the script for his next film, an immediately impending project for which he’s heretofore been unable to come up with an idea. Meanwhile his producer and crew, as well as the press, badger him for information about the movie they’re supposedly about to start shooting. But the memories haunt rather than help as the women, present and past, surround him and hound him.

As usually happens when Broadway musicals are adapted for the screen, especially the more modern ones, significant changes have to be made. So some of Yeston’s numbers have been jettisoned—unfortunate in terms of the music, but much less so for his lyrics, which even in the surviving songs come across as mediocre. But Marshall has also had to move away from the completely theatrical mode of presentation in what’s retained. He’s chosen to keep the musical segments in that form, even putting them on stages and having the performers play, in many cases, to audiences. But he situates them within more realistic, if flamboyant, period action (as in the film, the date is the mid-sixties). And in that material he often hearkens back to Fellini’s visuals. The result is an amalgam of “8½,” the Broadway “Nine” and Marshall’s rethinking, often all at once. The clearest example comes in the show-stopper “Be Italian” sung by Saraghina (here, Fergie of the Black-Eyed Peas), the beach prostitute whom Guido (here Daniel Day-Lewis) visited as a boy. One part of the sequence mimics Fellini’s visuals; but the other puts the character on a stage, accompanied by a chorus line, playing directly to us.

Fergie’s solo is a standout, but each of the women in the cast gets to strut her stuff. There’s Guido’s wife Luisa (Marion Cotillard), whose “My Husband Makes Movies” is a lovely tune with some awful words. And his mistress Carla (Penelope Cruz), at her sultry best in “A Call from the Vatican.” The director’s devoted costume designer Lilli (Judi Dench) gets a big production number in “Folies Bergeres,” while his gorgeous star Claudia (Nicole Kidman) comments on his “Unusual Way” during an evening stroll. Then there’s magazine writer Stephanie (Kate Hudson), who offers herself to Guido while celebrating the moviemaking he represents in the flashy “Cinema Italiano.” Even the regal Sophia Loren gets into the act as the director’s lovingly remembered mother with a simple lullaby, “Guarda la luna.” Apart from Fergie, none of the ladies is best known as a singer—though Dench has certainly sung on stage and Cotillard played Piaf—but each gets the job done.

Day-Lewis, on the other hand, fares less well. He hasn’t much chance to demonstrate his singing ability, but doesn’t shine when he does. And Guido’s habit of moping around in creative distress doesn’t afford the actor great opportunity to shine, though he seems more engaged in his scenes with Cruz and Kidman than elsewhere, and he has fun in a press conference early on.

Marshall keeps the pace headlong throughout, and he and editors Claire Simpson and Wyatt Smith combine the varied elements skillfully, while Dion Beebe’s widescreen cinematography captures all the glitz, only occasionally obscuring the effect of the choreography by failing to shoot the dancers in full form.

There will be those who dislike “Nine” because it fiddles with Fellini’s masterpiece. And others will criticize the movie for making alterations to the Broadway show. But if you don’t belong to either of those groups, you should find a good deal here to enjoy.