So I need multiple browsers running at the same time, more precisely multiple instances of the same browser of choice, that is a Firefox variant called Palemoon (I'll talk another time of this particular choice).
First of all, I'm using a Portable version, easy to backup as a directory tree, and reinstall / run from another Windows PC. No fuzzy discussion about the choice of the OS, please: most companies still use Windows, home PC, too, so go to the application.
Once the portable version is installed, just clone it as many times as required by your activity, and create separate shortcuts for each instance.
In the shortcut command line, add the following switch;
And you are done.
See also: http://kb.mozillazine.org/Opening_a_new_instance_of_Firefox_with_another_profile