Answer
Yes, using the 'Own Process' technique — copy the standard window's address from the address bar, RMB on the desired location in the Navigator, and choose New > Item; paste the copied address into the new item's parameters field, and append &PROCESS=<your_process_name> to it (any name you choose). This creates a second navigator entry pointing at the same underlying window, but running it in its own separate process context — that new entry can then have its own independent client layout/customization applied without affecting the original window at all.