How can I add more types of basemaps to the existing Add Basemap window?
I am using ArcMap 10.4 on Windows 10
These basemap are provided with ESRI, and developed in their own window. You cannot add basemap directly in this basemap window. However you can integrate other basemaps as services in the ArcMap.
You may use Portable Basemap Server, to create services for basemap and then add them in ArcMap.