Visual Studio supports horizontal and vertical tab groups and Tabs Studio now backs it up too. When you have two or more tabs open, use Visual Studio’s Window menu to create a new group:

New Horizontal/Vertical Tab Group commands
You can have as much groups as you want, but you can’t mix horizontal and vertical groups:

Three vertical tab groups

Two horizontal tab groups
IsGroupSelected property is added to all Tabs Studio controls to style inactive group. Default style sets text opacity for not selected group to 60%.
To move tabs between groups use Move to Next/Previous Tab Group tab context menu commands:

Move to Next/Previous Tab Group context menu commands