This edition of the Carnegie International, organized by Ingrid Schaffner, includes 32 artists and artist collectives — and very few unfamiliar names. The upside of this approach is that many of the artists here are midcareer and know, from experience, how to operate within the potentially homogenizing context of a large exhibition and create exceptional displays. Several here are outstanding, activating the Carnegie Museum of Art’s collection and making you think differently about art history.

On the outside of the museum, El Anatsui, the Ghanaian sculptor who has become one of the most imitated artists in Africa, has draped the upper facade of the entrance with a work made from his signature found bottle caps and printing plates sourced from a Pittsburgh printing press. The work treats the museum like a kind of body to be dressed with a garment. Inside the galleries, Ulrike Müller and Sarah Crowner use bright tiles, enamel, weaving and canvases sewn together to test the line between art and craft. Nearby, a terrific presentation of portraits by Lynette Yiadom-Boakye with cryptic titles suggests painting as a portal into the everyday lives of her characters, while Dayanita Singh’s installation with lush silver gelatin images bundled in cloth in India questions how history in the form of images is archived and stored.

The boundary between furniture and sculpture is playfully transgressed in Jessi Reaves’s fantastic full-room installation, where art and design blend. You’re encouraged to sit on the sculpture-furniture. If you make the pilgrimage out to Fallingwater, Frank Lloyd Wright’s “cabin” masterpiece designed for the family of Edgar J. Kaufmann, you can see Ms. Reaves’s sculpture on the terrace, made during a residency there: a lanky homemade shelving unit with an iridescent burgundy zip-on mantle that looks like a sadomasochistic vampire’s cape.

Back in the museum, Josiah McElheny, working with the curators John Corbett and Jim Dempsey, shows his MacArthur-award mettle with an expertly researched display. Curious musical instruments and documents relate to maverick composers like Harry Partch, Pauline Oliveros and Lucia Dlugoszewski, who created sculptural wooden instruments that are one of the standouts of the installation.