Is it possible to have 4 windows tiled on the screen, but have only one feature manager tree shown? Ths tree would be live and would switch as you picked another part window. This would take much less screen real estate when working with multiple documents. Right now it seems like the trees take up almost half the screen by themselves.
Or is is possible to just have the transparent flyout tree always visible instead of the traditional version? That way it would always be visible but you could still see your model behind it, keeping it large in zoom.
I think the OP is looking for something a bit more dynamic. The answer right now is No. However, SolidWorks has been trying to address similar requests for a long time. I'm not sure if a solution will be coming anytime soon, though.