Note that if you just want to open another instance of DevTools on an existing instance of DevTools (for example, just to see the generated html for the DevTools screens themselves), you can do this by just using the keyboard shortcut while you are in DevTools itself. On a Mac, this is Cmd+Opt+I. If I had realized this earlier, I probably would not have even gotten into the details for this post, which deals with (among other things) modifying the DevTools app. An interesting diversion, though.
While debugging DevTools can be done on just about any OS, the stuff below is on Mac OS.