You could do it in ArcGIS Online while creating a map.
http://www.cloudpointgeo.com/blog/2016/4/26/creating-a-multi-layer-basemap-in-arcgis-online
Add the other basemaps from http://server.arcgisonline.com/arcgis/rest/services
Do not Check "Use as BaseMap"
Keep the Options under the layer > Move to Basemap
Set visibility range for every basemap layer
Rename the Basemap layer, as desired.
Then you could save and share the map to web appbuilder or a story map.
Think Location