Não é possível mover um único local de pastas, a menos que o aplicativo permita isso. O Firefox, tanto quanto eu saiba, permite isso.
Leia este :
Modify profiles.ini to point to the new location - Advanced Firefox, Thunderbird and SeaMonkey 2 Note: This method does not apply to Mozilla Suite/SeaMonkey 1.x, which uses a different system for keeping track of profiles. Firefox, Thunderbird, or SeaMonkey 2 should already be installed on the computer where you are moving the profile and a profile folder and profiles.ini file should already exist. This method is recommended for advanced users only since it can be tough to troubleshoot. Mozilla applications can be very finicky about the contents of the profiles.ini file. They normally do not ignore bad entries, regardless of their position in the file. Create a new, empty folder in the desired profile location with the name you wish to use for the new profile, for example, D:\Mozilla\Firefox\Profiles\newprofile Copy the entire contents of the profile folder you are moving into the new profile folder you just created. If you copied the old profile from a CD, remove the write-protection from the copied files. Find the profiles.ini file (it will be located in the default profile folder path) and open it in a text editor. (Optional) Change the "Name=" line to the name of the new profile folder you created, e.g., Name=newprofile Change "IsRelative=1" to "IsRelative=0" (non-relative/full path) Change the "Path=" line to the actual location of the new profile folder, e.g., Path=D:\Mozilla\Firefox\Profiles\newprofile. If you're using Windows non-relative paths use back slashes while relative paths use forward slashes so you may need to change the direction of the slashes too. If you are moving a profile from its default location, the original profile folder can now be removed. If you're using Thunderbird, check that you can see the folders for each account. If they're missing, use the browse button for the local directory in Tools -> Account Settings -> Server Settings and Tools -> Account Settings -> Local Folders to specify the correct account and mail directories. Caution: Incorrect editing of the "profiles.ini" file can cause a "already running but is not responding" error if the profile cannot be found (bug 278860).
Isso precisa ser específico do aplicativo, você também pode querer examinar edições portáteis de software projetadas para serem instaladas em dispositivos USB, essencialmente não usando nenhuma propriedade do sistema, mas salvando tudo em seus próprios arquivos.
Editar: Você também pode usar hard links .