+1, although a furtherance of this request, as currently the left/right sides are used for the display area of various plugins…
If Tabs on the Left/Right was to be considered, perhaps the display of the plugins themselves could be more modular and resizable.
E.G. The Tabs on the Left/Right would be inside a dockable container that could be resized in all directions. The container could have a scroll bar or Up/Down buttons to bring other tabs into view that wont fit into the current height. Likewise the plugins would be inside a dockable container that could be resized.
Thus you might have something like:
|[↑][↓] |01| Edit Area
|[File 1 ]|02|
|[File 2 ]|03|
|[File 3 ]|04|