Make it new: with a four-part show inaugurating its sleek facility on the Bowery, the once-scrappy New Museum faces a tough question: can its cutting edge stay sharp?

When Marcia Tucker founded the New Museum of Contemporary Art in 1977, following a dustup with the board of the Whitney Museum in which she lost her curatorial position, she wanted to create a radically different kind of institution. In the museum's early days, all staff members received the same salary, rotated tasks and shared equally in decisions. While this administrative model quickly proved untenable, the New Museum's early focus on alternative and antimainstream approaches to art remained an important part of its identity through the 22 years of Tucker's tenure as director.

The new New Museum, which opened its doors last December in a celebrated new building on the Bowery designed by the young architectural team Kazuyo Sejima + Ryue Nishizawa/SANAA, is another kind of animal altogether. As sleek as a mini-MOMA, and just as carefully attuned to "naming opportunities," with every component, from the stainless steel visitor desk to the restrooms and back stairs, emblazoned with a contributor's name, the New Museum is now poised to do battle with its larger New York competitors on its own terms.

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The title of the opening exhibition, "Unmonumental," seems a tribute to the museum's historical mission, suggesting a rejection of crowd- and collector-pleasing grandiosity in favor of something more marginal, modest and subversive. However, the art inside, though carefully tattered and unpolished, is not really "new" or particularly alternative, especially considering the long gallery pedigrees of many of the artists on hand. Opening in phases over 11 weeks, the exhibition eventually has come to comprise four parts, each layered over the others. The four sections were curated by Richard Flood, Laura Hoptman and Massimiliano Gioni, all members of the museum's revamped senior staff. The first, which opened along with the museum itself in early December, is devoted to "The Object in the 21st Century" and consists of freestanding assemblages by 30 artists. "Collage: The Unmonumental Picture," which opened Jan. 16, is composed of wall works by 11 artists that have been installed in the galleries to surround the sculptures from phase one. The third and fourth, "The Sound of Things: Unmonumental Audio" and "Montage: Unmonumental Online," opened mid-February.

By far the most extensive section, "The Object in the 21st Century" presents works that approach the found or fractured object in various ways. Some artists, like Shinique Smith, whose bundies of rags evoke Arte Povera pioneer Michelangelo Pistoletto, offer accumulations of found objects. Other works, like Rachel Harrison's anti-homages to various pop icons, mingle created elements (here amorphous abstract forms in polystyrene and cement) with photographs and readymade objects. There are also spare juxtapositions of things manufactured, one example being Martin Boyce's We climb inside and everything else disappears (2004), a lounge chair frame set on its side and threaded with a coiled yellow tube. Other works are fabricated rather than readymade, and find common cause with the theme in their fragmentation or unconventional use of materials. For instance, Urs Fischer's roughly modeled wax female nude figure is literally a candle that was gradually melted throughout the course of the exhibition. Also figure-based is the work of Matthew Monahan, whose wax and painted foam constructions suggest fractured and mutant Art Deco figures.

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Certainly, as even the curators acknowledge in their catalogue texts, this is not a new approach to art. Indeed, they offer multiple genealogies, linking the works on view to Duchamp, Dada, Arte Povera, assemblage, the Combines of Rauschenberg and the chance procedures of Cage. In a more contemporary vein, they invoke the esthetic of ruins set off by the attacks of 9/11, the cacophony of the information age and the melanges of MySpace. They offer correspondingly multiple interpretations, making reference to Baudrillard's theory of the simulacrum, Rosalind Krauss's seminal essay Sculpture in an Expanded Field and Nicholas Bourriaud's Relational Aesthetics. The works themselves fly out in many different conceptual directions, from deconstructing modernist esthetics to spoofing gender politics and consumer culture to riffing on private histories and fantasies. And some are simply inert, not yielding much of any meaning to a puzzled museum visitor.

Interestingly, the installation of the scattered sculptures, which in phase one seemed overly crowded and confusing, gained a certain amount of clarity with the addition of the collages. Each collage artist has been given an entire wall. The biggest transformation came on the third floor, where Wangechi Mutu has unfurled a whole universe across the biggest wall, which she painted brown and outfitted with a planetary orb composed of mounds of stuffed fabric, fake fur and aluminum foil. Establishing a low horizon at floor level is a mountain range made of layers of brown tape, while the brown "sky" above is filled with celestial phenomena created by strings of beads and scatterings of floating "stars" made up of tufts of fur affixed to cutout photographs of a skinned pig. Mutu's apparition has the effect of turning the sculptures on the floor in front of it, especially Rebecca Warren's clay and bronze blobs and Fischer's evocation of Excalibur stuck in a pile of dirt, into features of some weird lunar landscape. The other truly inspired intersection of phases one and two occurred in the narrow space behind the elevator on the second floor, where Kristen Morgin's decaying clay vessels play off Kim Jones's reworked photographs of his Mudman character, which, thanks to the addition of tight ink drawings of cartoonish appendages, seem likewise in a state of organic decomposition.