The character of America’s two most prominent diamond and jewelry districts—in New York City and Philadelphia—may change dramatically as developers increasingly scout them for non-jewelry tenants. In New York City, speculation is centered on the intentions of Gary Barnett, the former diamond trader who built and still owns the 47th Street International Gem Tower. According to DNAinfo and public records, Barnett’s company, Extell Development, plans to demolish two 47th Street buildings it recently purchased, 2 West and 10 West. (Tenants have already vacated those buildings.)   The company will also knock down two nearby buildings—562 and 564 Fifth Ave. between West 46th and West 47th streets—as well as six buildings on West 46th Street. There are rumors that Barnett owns other buildings on 47th Street, which have also been emptied. No one knows what Barnett will do with th