Multitracker,
Deactivate RB and BIAB registrations before you re-install. (You'll need to be connected to the internet to deactivate.) Doing this will protect your three activations.
I have not done that and reinstalled, the Authorization on the one machine remained the same all by itself.
Apparently Authorization is tied to the specific machine's identity code and NOT ABLE to assign two authorizations onto one machine.
I assumed that was because the Authorization is tied to the Machine and not the install of the program, once the proper code is inside that one folder, the reinstall apparently did not overwrite it.
But I did the reinstall *right overtop* of the old one, I did not go in there and do any uninstalling or deleteing of anything, why bother? The Installer will only overwrite those files of the same name in there, and does not seem to overwrite files such as user prefs, etc. to include the Authorization. At least, that's how its been working for me here.
--Mac