Can you have multiple groupings on a view?
Create multiple view pages in a single View definition and assign each with the same basic paths, but a different last segment eg. Node/%/Group1 &amp; Node/%/Group2.
For each view select a menu item in the second column and set the type to menu tab.  Provide the name to display on each tab.  
Set one of the pages' menu to default menu tab so it will show up first.  set its parent to already exists.


When you enter the path in the URL, you should get the default page displayed with the menu tabs above the view block.