Install OS X Applications and Library directories on external drive

Wondering how could I set some sort of partial OS X installation on an external drive, I searched Google only to find that I may be the only one looking for this. The goal is to get both the Applications and Library directories (those from OS X installation's root, not user's) to run them on any Mac, always keeping the applications' preferences in the Library directory, on the drive.

You may see that as some sort of partial OS X installation.

Is this possible and, if so, how ?