You need to edit the batch file to include these commands;

Here is an example (on one line only); -no-remote -new-instance -new-window

https://developer.mozilla.org/en-US/docs/Mozilla/Command_Line_Options

Usage: C:\PROGRA~1\MOZILL~1\firefox.exe [ options ... ] [URL]
      where options include:
 
 -h or -help        Print this message.
 -v or -version     Print Firefox version.
 -P <profile>       Start with <profile>.
 -migration         Start with migration wizard.
 -ProfileManager    Start with ProfileManager.
 -no-remote         Do not accept or send remote commands; implies -new-instance.
 -new-instance      Open new instance, not a new window in running instance.
 -UILocale <locale> Start with <locale> resources as UI Locale.
 -safe-mode         Disables extensions and themes for this session.
 -console           Start Firefox with a debugging console.
 -jsconsole         Open the Error console.
 -browser           Open a browser window.
 -new-window  <url> Open <url> in a new window.
 -new-tab     <url> Open <url> in a new tab.
 -preferences       Open Options dialog.
 -search     <term> Search <term> with your default search engine.
 -setDefaultBrowser Set this app as the default browser.

HI Fred and thanks for the response. I added: "-no-remote -new-instance -new-window" to the command line, and firefox did indeed open a new, private window. However, it only did so after displaying this error: "firefox is already running. This old firefox process must be closed to open a new window." I clicked ok, and it did just that, closed the old instance and opened a new, private window.

I had hoped to be able to keep the old process while opening the new one. Is this possible? Thanks r

Please copy the full batch command and post it here.