Is it possible to rearrange the tabs within a document? I can't seem to drag and drop the tabs.

You bet!

In order to re-arrange or organize the tabs at the top of the document view simply follow these steps: 

1. Access the hamburger icon (the horizontal stacked lines to the left of the tabs).
2. Hover your cursor over the title of the tab you'd like to move.
3. Pick up the the title you'd like to move and drag it to its new position in the list of titles.  
4. Repeat step 2 & 3 until you're happy with the tabs' organization.