<< Attached picture is exactly what I want to achieve. >>
It seems BIAB can do this now and have multiple docked screens. I may be missing something. I'll be glad to provide loading instructions if the images I've attached are what you're trying to get.
Unless I'm mistaken, those aren't docked, they're floating windows placed on top of each other, i.e., the other panels don't shrink and allow the additional panel to share the space within the parent window.
I think the only window which docks like that is the mixer window, which can be docked and un-docked with the icon in its top-right corner.