“There’s a lot at stake here, for us and for him, and I really didn’t want to get this wrong,” Ms. Goldsmith said.

Ms. Goldsmith works in a quiet, sunny corner office in Midtown Manhattan, surrounded by Seussenalia. A stuffed Lorax sits in the window, and a framed photo of Mr. Geisel on his 80th birthday hangs above her desk. In a filing cabinet, in what she calls the “magic drawer,” she keeps fragile early editions of books like “Hop on Pop” and “If I Ran the Circus.”

Ms. Goldsmith started working on Dr. Seuss books in 1978. She remembers her first encounter with Mr. Geisel, a tall, imposing figure with a wicked sense of humor. “I had no idea what to call him when I first met him,” Ms. Goldsmith said. “No one else called him Dr. Seuss.” He finally noticed that she was awkwardly avoiding using his name, and told her to call him Ted.

She worked with him for the next 11 years. Toward the end of his life, when he was too ill to finish coloring in the final pages of “Oh, the Places You’ll Go!,” he called Ms. Goldsmith. She flew out and stayed at his home for several days, coloring under his direction.

By the time Ms. Goldsmith met him, Dr. Seuss was already a publishing legend. But his instantly recognizable artistic and literary persona — the tongue-twisting, anarchic rhymes and hallucinatory drawings — had evolved over many decades, as Mr. Geisel pursued a career in advertising, then made a name as a political cartoonist.

Though he published his first children’s book to acclaim in 1937, it wasn’t until 20 years later, with “The Cat in the Hat,” that Mr. Geisel gained blockbuster status, and Dr. Seuss became a beloved and influential brand. The next few years were prolific. Mr. Geisel wrote “How the Grinch Stole Christmas!,” “Yertle the Turtle,” “The Cat in the Hat Comes Back” and “One Fish Two Fish Red Fish Blue Fish” in quick succession.

It was then, in the late 1950s or early 1960s, that Ms. Goldsmith and the Seuss archivists believe that he wrote the story about the pet shop. The children in the book are virtually identical to the boy and the girl in “One Fish Two Fish.” He was juggling multiple projects, and may have set it aside for later. Or it may have been the jumping-off point for “One Fish Two Fish.”