The Add-Ins Tab is a stop-gap transition measure. Its purpose is to allow use of older Add-Ins in Ribbon Versions of Word.

It has two built-in groups: Menu Commands and Custom Toolbars. You can place these groups on the QAT. Individual commands can be put on the QAT but not from the custom toolbars.

You can, using XML, modify the Ribbon and put tabs of your own with your own menus on them. You can copy these to the QAT.
Modifying the QAT and Ribbon in Microsoft Word
Customize the Ribbon (It doesn't take rocket science)

Take a look at the CC⁄V⁄BM & DP Tools Add-in which makes a modification to the Add-Ins tab. Controls added there, through XML, can be added easily to the QAT by right-clicking on them.