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When Harper Lee’s “Go Set a Watchman” hits bookstores in July, it will face sales competition from another long-lost manuscript by a beloved author: Dr. Seuss.

Random House has announced the publication on July 28 of “What Pet Should I Get?,” the story of a brother and sister searching for the newest member of the family. The manuscript had been in a box that was discovered in the home of Dr. Seuss (otherwise known as Theodore Geisel) in the La Jolla section of San Diego, shortly after his death in 1991, and set aside. In 2013, Mr. Geisel’s widow, Audrey, and longtime secretary and friend, Claudia Prescott, went through the box and found the nearly complete manuscript, along with other unpublished work.

Cathy Goldsmith, the vice president and associate publishing director at Random House’s children’s publishing division, said in a statement that the book seems to have been written between 1958 and 1962, given that the brother and sister are the same as those in “One Fish Two Fish Red Fish Blue Fish,” which was published in 1960.

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Mr. Geisel typically did his illustrations as black-and-white line drawings, with color to be filled in later, a process that Ms. Goldsmith, who worked with him on “Oh, the Places You’ll Go!,” will oversee. “I know he is looking down, watching over the process, and I feel a tremendous responsibility to do everything just as he would have done himself,” she said.

Random House plans to release at least two other books based on the recently rediscovered materials, with publication dates to be announced later.