From our internal KB article, which I adapted from @jay-cummin's post here, and then wrote some scripts to make using them quick and painless:
As many of you have discovered, at times you can’t switch from ArcGIS Basic to ArcGIS Advanced because the radio buttons in ArcGIS Administrator are disabled:
Fortunately there is a workaround, set the license level in an environment variable first and then run ArcMap/Catalog. We’ve placed scripts for this in
ArcMap-Advanced.bat run ArcMap using Advanced (ArcInfo) license
ArcMap-Editor.bat run ArcMap using Editor (ArcEditor) license
ArcMap-Viewer.bat run ArcMap using Viewer (Basic) license
I actually prefer the workaround to the original method: you don’t have to close all your sessions down first just because you want to run an Advanced-only tool for 5 minute job like Create Random Points, and you can run Advanced and Basic side by side at the same time.