Base maps are the lowest level in the device. As far as I know, you cannot overlay your own data directly onto these without overlaying the base map. This has to be the case, otherwise you wouldn't be able to use your own raster maps, for example. Consequently, the order of the elements from bottom to top on the device is as follows:
- Base map
- Raster maps
- Vector maps
- Device points, device lines
If you place any vector elements on the base map, they are integrated into a kind of tile structure, the basic color of which is the well-known olive, which I could only change with raster maps or by using polygon shapes, which then overlay the olive base tile.
The only thing you can do is "reconstruct" the base map using your own vector elements, provided you can find the data for it. There are many openly accessible data sources for this, especially in the USA.