At the moment it is not possible to open several windows of the new output log. It is however possible to use the standard log window together with the new output log (as you can see in one of the screenshots).
This is a problem that all “tool windows” in UE4 have. Their current workaround is to just add 4 menu entries for the same thing into the main menu. So you have “Viewport 1”, “Viewport 2”, etc. as menu entries, which is pretty horrible as far as UX goes.
But that is a very easy solution that I might add for the new log window.