The Seurat and Puryear shows may be the biggest draws at the Museum of Modern Art right now, but gallery-goers shouldn’t overlook two other intriguing exhibitions that draw on the museum’s own collections. “Multiplex: Directions in Art, 1970 to Now” employs three broad categories as a hopeful means of organizing a bewildering assortment of post-1970 art. The works in “New Perspectives in Latin American Art” meander in a different way — physically, across two floors — with artworks spanning nearly eight decades. In both cases, elegant, spacious installations add a measure of coherence to diverse selections of art.

The fifth in a series of annual installations of contemporary art, “Multiplex” cuts a wide swath. As the title suggests, the exhibition is a cacophony of expressions, connected only by their relatively recent vintage and their loose conformity to the categories of Abstractions, Mutability, or Provocation. The result is poignant testimony to what critic Arthur Danto has called the “radical diversity” of our time: While the more than 70 paintings, sculptures, drawings, prints, photography and media works reflect a common faith in art’s expressive potential, they hardly agree on what this potential might be.

Installed in several white-painted galleries, the abstract work ranges from a 1972 canvas by Robert Mangold to a 2000 video of shifting, psychedelic colors by Jeremy Blake. Some paintings stand out for their formal vigor; in different fashion, the interior shapes of the Mangold and a 1976 Elizabeth Murray canvas push playfully against their physical edges, while several other paintings — by Terry Winters (2002), Thomas Nozkowski (2001), and Carrol Dunham (1983–85) — resonate with sinuous internal tensions. In keeping with the postmodern trend of mixing disciplines, paintings by Thomas Scheibitz (2003), Julie Mehretu (2003), and Mark Grotjahn (2004) draw upon traditions of graphic design, their handsome patterns showing little weighting and pacing of rhythm. Utterly inert in its coloration is Andy Warhol’s series of eight “Camouflage” screenprints from 1987.

Roni Horn’s large, seemingly molten chunk of red-orange optical-grade glass (2002–04), placed unceremoniously on the floor, has a luscious appeal: You can hardly resist touching it. By comparison, the tension between fluidity and stasis in Lynda Benglis’s twin sculptures (1970–74) — identical except for their bronze and aluminum castings — feels a bit calculated. Dorothea Rockburne’s huge piece from 1970, consisting of three rolls of paper, variously folded around or covered by chipboard sheets as they unwind down the 20-foot height of a gallery wall, is too clever by half; like the museum’s own architecture, it serves best as a tantalizing foil for other goings-on.

Other notable abstract pieces include Tobias Putrih’s two sculptures of layered corrugated cardboard (2005), which resemble giant, porous Chinese scholars’ rocks, and Andreas Gursky’s panoramic photograph (2005) of a racetrack winding madly through a Bahrainian desert.

Gallery walls, appropriately enough, turn gray for Mutability, a category the wall text describes as involving “a shifting perception of reality and self.” Here feminist art is much in evidence. Snippets of text and drawings, reflecting sexist and racist attitudes, line three walls of Nancy Spero’s installation from 1979, while Louise Bourgeois’s enclosure of suggestive, dangling objects within a circle of folding screens (1986) evokes issues of privacy and entrapment. A suite of 14 intimate, photographed self-portraits by Adrian Piper (1971) enlivens another wall.

David Hammons’s 2005 sculpture, a stone adorned with real, cross-cropped hair, eerily conjures the depersonalizing stare of racism. In Rodney Graham’s installation (2003), a 35mm film captures picturesque snowflakes accumulating on an antique typewriter, but the highlight is the projector, a monstrous, purring machine that would be at home in a Buck Rogers movie.

On the whole, the works in Provocation are surprisingly tame, considering the explicit sexuality and violence sometimes on view in galleries in recent years. Lisa Yuskavage’s painting (1996) of a bizarrely distorted nude addresses issues of the female self-image and the violating gaze. Once again a canvas (1999) by Chris Ofili incorporates balls of elephant dung, along with glitter and map pins, as not very subtle tokens of ethnic decoration. In this company, Philip Guston’s simple but robust painting of a Klansman (1972) serves as a lonely holdout of rigorous modernist composition.

Some provocations amount to indulgent vignettes: Bruce Nauman makes faces — with the aid of his hands — in a series of four yellowish screenprints (1970), while Gilbert and George celebrate a dapper dissolution over the course of a 12-minute video (1972). More engaging is Clemens von Wedemeyer’s video from 2002, which revisits the Laurel and Hardy classic “Big Business” and its one-upmanship of destruction; if the demolition seems all too gleeful, an accompanying documentary video explains that the actors were real-life prison inmates. The single most disturbing work may be Cheryl Donegan’s 1993 video of herself gulping and spitting a stream of milk, an act that becomes increasingly sensual, arbitrary, and desperate. (Milkboarding, anyone?) Like many pieces here, it’s energetically executed, crackling in its effect, and totally scattershot in its intimations.

Most museum visitors are probably unaware of the depth of Mo-MA’s commitment to Latin American art, but the museum’s holdings in this field are in fact the world’s largest, dating back to its first acquisition in 1935. “New Perspectives” presents some 200 Latin American and Caribbean works acquired over the past decade, and it avoids — no doubt deliberately — the usual superstar roundup: There’s nary a Rivera, José Clemente Orozco, Siqueiros, Kahlo, Lam, Matta, Marisol, nor Botero.

Introductory wall text emphasizes the independent development of Latin American artists, who were investigating Constructivist issues when Abstract Expressionism ruled supreme in America. Later, during the heyday of the cerebral coolness of Pop and Minimalism, many Latin American artists turned to political activism. Visitors expecting abundant signs of social ferment, however, will be disappointed. Many of the drawings, paintings, photographs, prints, and sculptures have an introspective, cosmopolitan air, though tinged with an earthier lyricism than their North American and European counterparts.

The very earliest piece, a 1930 abstraction by Joaquín Torres-García (Uruguay) adds modulated tones — and a wholly original dimensional warmth — to a Mondrian-like grid of yellow, red, and black rectangles. Brazilian Lygia Clark’s small collages of colored cardboard (late ’50s) and metal-disc sculptures (1960) have a lithe monumentality.

Two lively gouaches from the late ’50s by Hélio Oiticica (Brazil), discreetly urgent in their irregularly tilting rectangles, hardly prepare us for his boxy construction from the mid-60s with its rawly painted surfaces and interior coves filled with rocks and earth.

Numerous works from the ’60s and ’70s reflect a variety of approaches: the Venezuelan artist Gego’s finely lined etchings exploring order and disorder; the furtive images of Mira Schendel (Brazil) with their wisps of lines, tiny isolated letters, and dainty perforations, and the organic webs and neat, alphabet-like clusters in the drawings and prints of León Ferrari (Argentina).

Politics do come to the fore in more recent works. The 1980 sculptural installation by Victor Grippo (Argentina) features real beans bursting from sheet-lead containers as a rather obvious metaphor for growth and liberty. A series of screenprints and lithographs from 2006 by Santiago Cucullu (Argentina) encompasses ambiguously threatening images — some of them torture scenes — within swirls of vivid color that could be flames or textile patterns.

The most intriguing of a number of cartoon-inspired pieces is an untitled work from 2003 by Arturo Herrera (Venezuela), who cut and pasted tendrils of newspaper comics into a veiny scrim depicting a fantastic castle. Another witty work, the large 2005 photograph by Vik Muniz (Brazil), shows an affection for humble bric-a-brac taken to its extreme; it depicts the arrangement of a vast room of junk into the likeness of a Caravaggio painting.

The two exhibitions at MoMA offer occasional, fascinating parallels. A portfolio of screenprints of reductive black shapes by Gerd Leufert (Venezuela), published in 1985, formally anticipates Allan McCollum’s 2006 edition of digital prints in “Multiplex.” Mr. Ferrari’s incorporation of three-dimensional filaments into a drawing of swirling lines (1963) finds a counterpart in Lin Tianmiao’s ephemeral, thread-enhanced lithograph from 2006. Such echoings suggest the flip side of the cutting edge: What goes around comes around, and sometimes sooner than you expect.

“Multiplex” until July 28, “New Perspectives” until February 25 (11 W. 53rd St., between Fifth and Sixth avenues, 212-708-9400).