What you could try* is to use the new Split Container (v8.1.18) to mimic the behavior of a docked window. In my head, I would probably define one of the docks as I normally would (probably the one that would be used more) and then for the other one, you can drop your contents into a split container that you would set the size of to mimic opening and closing it.
Another thing you can try is create a view you’ll define as a dock and then inside that view, have a container that you will toggle the display property to simulate opening/closing another dock.
The last thing I can come up with is to open a popup window (with a docked view) with the position property specified, like so:
EDIT: Another idea I have is to use the new system.perspective.alterDock function available in v8.1.19 to open a dock and then when you would trigger your second dock, you can change the size of the one dock that is already open to “open” the other one (just make it visible to the user).
*Disclaimer: Just ideas, have not implemented this before so I don’t know if they work or not