John Nugent spared no expense customizing his Andover, Mass., home for his family. For his sports-loving children, he built a full-size indoor basketball court with a scoreboard, a 30-second shot clock and three rows of bleachers. Downstairs, there’s a bowling alley with a vintage scoring machine, and an indoor pool with a water slide. On a wall near the pool, there is a mural with images of Mr. Nugent’s children, along with the family’s dogs, cats, bird and pet rabbit.

Then the children grew up and moved out, and Mr. Nugent...