This idea has been merged with Create Our Own Basemaps in ArcGIS Online.
Basically I would like to use the imagery world service, then have multiple layers on top of that. Then save all of that as a basemap.That way all those layers can be used together and not seen by the end users. Then add various operational layers on top of that basemap.
Esri tells me that basemaps don't support multiple layers. If there are multiple layers it will default to the bottom layer. Which is the behavior I've seen. Just doesn't seem right that you can't create your own basemap.
Esri refered me to the following enhancement request:
#NIM088516 Allow users to create custom basemaps in ArcGIS Online by adding more than one layer. Currently Basemaps need to be single-layer web maps created with the ArcGIS.com map viewer or ArcGIS Explorer Online. If we reference a multi-layer basemap, only the bottom layer will appear. This prevents users to create their own basemaps by adding two layers.