It took a while to make a good title for this post and I still am not sure it covers everything so I'll explain. (Using PHPStorm 2017.2.1 on Xubuntu 17.04.)
With multiple monitors I was trying to have the main IDE window on one monitor and all database windows (1: the database tool window with database connections, 2: the editor tab for SQL statements, 3: the editor tab for a single table / query results, and 4: the database console with its Output and Results tabs) on the other monitor.
I can drag the editor tab outisde the main IDE and I can use the float or window mode on the tool window and console, but that results in extra windows, including extra task bar icons.
So I was trying to make them dock into a single window. And that is not possible.
I have read several topics on having multiple IDEs looking at a single project, which apparently is not possible and also quite difficult to implement.
Maybe it's easier to look at it as a new window that accepts docks so I get a second but single window with editor tabs and a database tool window and a database console window?