POTOMAC, Md.—On a bright spring morning, Debbie Driesman and her interior decorator surveyed progress on Norton Manor, the 40,000 square-foot house she's building with her husband, information-technology entrepreneur Frank Islam. To make way for the French chateau-style manse, the family bought two houses on adjacent 4-acre lots and invited the local fire department to destroy them. For practice.

The manor, in suburban Washington, features a reflecting pool (just as the Capitol does), east and west wings (like the White House)...