Yes, this is possible to do using a relatively simple yet unknown workaround...just create a new Web Mapping Application.
When you Add Item under My Content, choose "An application" and then add the URL of your webmap as it appears while open in ArcExplorer Online. Something to the effect of this:
http:://myorganizationname.maps.arcgis.com/explorer/?open=bbc920a87c7f43309995e3788047548c
Then title, tag n' save and you should be good to go. Hope this helps!