I don't think SS got theirs built but there are multiple replica White Houses in the US and abroad (one very large one in China owned by a theme-park mogul).

There are multiple supposedly carbon-copy or close to it replicas of the White House in the US and abroad (one very large one in China, owned by a theme-park mogul).

https://greatawakening.win/p/11SJoRrpWb/chinas-white-houses-time-2010/