It can be done - to convert Knoppix to an ordinary multi-user system.
Knoppix isn't Debian. It is based on Debian. And it is a strange mix of different Debian versions that generally cause problems for people who try to install it to a hard disk.
You can not install Debian from the Knoppix disc. However, you can go to the debian website at debian.org and download an install disc iso for any of the Debian versions. If you have high speed internet then I suggest downloading the net install disc iso. However, if you are on dial-up or don't have Internet access where you intend to install, I suggest disc 1 of the install discs (all of the discs are not needed and generally not a good idea to download unless you are planing on going where you will have no Internet access, and maybe not even then). Also, you will find that there are different versions of Debian available, I suggest staying away from "stable" for anything except a mission critical server system, it is too old. I suggest "unstable", although you might even want "testing". Don't be fooled by the names, "unstable" is far more stable than anything that Microsoft ever released. You can also pick from builds for various hardware. Knoppix uses the i386 code. if you have a typical PC you may want to use that or go with a 64 bit version for Intel or AMD cpus.
Once you have done a desktop install of Debian you will have multiple user support. You can then choose to install any or all of the application that are included in Knoppix, or pick from a huge selection of other programs in the Debian repository.