A 19th-century Long Island farmhouse is redesigned for a modern family. In the living room, the custom sofa is upholstered in a Mark Alexander fabric, the same Arabel Fabrics linen is used for both the curtains and the armchair, the Thebes-style caned stools are vintage, the cocktail table is by Dos Gallos and the abaca rug is by Stark; the ceiling is painted in Super White by Benjamin Moore, with beams in Armory by Pratt & Lambert.