Plug-ins are your friend for setting custom default values. I have not messed with this one but I have with other parameters. The principle is to identify the id/name for the button in question then either add the command to the InheritParentTemplate plug-in (this is convenient since it is already working anyway), or do your own custom plug-in (use the inherit one as a starting point).
Like this you could write unlimited amount of custome settings based on parent id, action, etc...
Here is some help to get you started:
1) the identifier for the button is $_REQUEST[’stay’], the value that represents the create a new doc is 1.
2) the button is looking for the $_REQUEST[’stay’] value in order to set the status of the push button. Add this into the plugin to tell it to select the "add another" option:
In order to control when to use this you could set a few logic statements to look to see if the document belongs to a certain parent, uses a certain template, or if it is editing or adding new documents.
Hope this helps and gives you a good idea of the possibilities. Also I am not sure but the ManagerManager plug-in may also have control over that button which will make it easy to manage and customize.