The Medieval Hall in the middle of the Met is the original building:
American architect Calvert Vaux was given the commission to design the first wing of the museum: The Medieval Hall, which is in the center of the museum complex today. It was completed in 1880, but is now surrounded by extensions on all sides. You can still see Vaux’s original Victorian Gothic façade in various places, like in the Robert Lehman Wing.
The American Wing was once a freestanding building:
The neoclassical facade of the American Wing, curiously built into the wall of Engelhard Court (Gallery 700), was actually a freestanding building facing an exterior garden for fifty years, until it was enclosed in 1980. The facade was rescued from the Branch Bank of the United States, located on Wall Street, before that building’s demolition in the 1920′s.