Operated as the English House from about 1907 to 1938, the house on the market at 145 North Street in Catskill offered boarding year-round with a promise of mountain views and light and airy rooms.

From the street, Anne Spratling and John Ayris’s home looks like a classic English country house. But its backyard holds a secret. The couple have doubled the size of their roughly 200-year-old ...