Q:

How to raise one DialogFragment above another? 

Say I have several dialog fragments that are shown in response to messages and events that can arrive in any order.   Normally, the last dialog shown will be on top.   Is there a way to show a dialog fragment under an existing one, or change their z-order after they are shown? 
It should be pretty rare for my app to show more than one dialog at a time, but it could happen.   There is one particular dialog that should always be on top whenever it's visible. 

A:

A dialog creates an application sub-window.  Android's window manager (WindowManagerService) automatically computes window's z-order depending on its type and stores it in WindowState's mLayer field.  Internal Android classes have access to this field and change window's z-order sometimes, but this API is not exposed to Android SDK.  So it seems that the only way to affect dialog's z-order is to recreate it. 
Everything I wrote above is just a result of a brief investigation of Android's source code so I may be wrong.  And maybe there's some hacky way to do what you want using reflection and accessing private fields and methods.  But I'm not sure it's a good idea to try and do it.  In my opinion it would be better to have just a single dialog or even activity, and manage fragments within it.