In the late 1960s, when San Francisco lawyer Frank “Sandy” Tatum and his wife, Barbara, set out to build a family beach home, their vision, for a house that could sleep 12, was large. Their slice of beach on Monterey Bay wasn’t.

Undeterred, the Tatums hired William Turnbull Jr. to design a roughly 1,600-square-foot house on Potbelly Beach in Aptos, Calif., approximately 80 miles south of San Francisco. To maximize the living space, Mr. Turnbull, then just starting what would become a notable architectural career, devised a modern, three-story home anchored by what he called a “sleeping machine,” a white, rectangular structure that housed the bedrooms and bathrooms, said Shelley Tatum Kieran, 60, the youngest of the Tatums’ six children. Two staircases and an open-plan living room with floor-to-ceiling windows flank that core sleeping block.