Answer
No, it is not possible to customize the Add Basemap command in ArcMap using ArcObjects. For example, when the user adds new basemap thumbnails other than the thumbnails present in the Add Basemap dialog box. This is not possible because the command’s source code is considered to be an out-of-the-box functionality, and as such, its methods and properties are not exposed via ArcObjects. Therefore, the code cannot be changed or customized.