It would be really nice if mupdf could have command line flag telling it to open a pdf in an existing mupdf window if already in existence, or even in a configuration file for the user. VLC as this as an option and is really nice in Dual screen enviroments and just as nice in single. Scenerio: You have your program on screen one, ex. Firefox, your browsing and your looking through pdfs, you click on the pdf link and it opens with external program: mupdf. then you drag that to your screen two and keep it there, you continue scrolling in FF and see pdf number two, you then click on it, FF calls external program: mupdf, it opens on screen one and you have to drag it to screen two again and close pdf one. I do this all day long, currenly with evince and it works, but I like the speed and functionality of mupdf. Support for both Windows and Linux would be nice.
Behaviour like this has to be implemented using some form of inter-process communication, which is both non-portable and non-trivial to add to a simple program like the mupdf x11 viewer. One possible workaround in your scenariou could be to set the DISPLAY variable when invoking mupdf to use the screen number of your second display (i.e. DISPLAY=:0.1 instead of DISPLAY=:0.0)