Is there a way to create a nested App menu for Splunk (the default App menu)?
I'm not sure exactly what you have in mind, but you can edit the default navigation XML through Manager > User Interface > Navigation menus. See the topic about navigation XML in the Building Apps and Views for Splunk Web manual.
That works for most menu items. Not sure the default Splunk gui menu items such as the App menu. This kind of gives some insight on how to go about doing it. http://answers.splunk.com/answers/7891/app-manager-jobs-logout-menu