OK, then your question is: If I plug external disk into my laptop, can I make it work as "extension" to the main one?
You can keep your work files on that external drive (downloads, music/movies/photos). Assuming you're running Windows 7/8/10, you can include the folders into libraries, and have almost instant access to them. You can even install most of the programs to the external drive (but on some programs, some files still must be copied to the boot drive).
I would not recommend moving your profile directory to the external drive - it will make logging in more problematic. But you can move almost all other system folders there.