OMG, with a persistent home, you can use apt-get! (Thanks to the magic of Unionfs and the wizardry of Klaus Knopper.)

After creating a 300MB persistent home on hda2, then rerunning Knoppix using the cheatcodes

knoppix lang=us keyboard=us home=/mnt/hda2/knoppix.img

Knoppix brought up a new (to me) ncurses-based dialog box warning of the danger of scripts that can be run from it. It asked if I really wanted to use that image. It said, these capabilities can be selected separately; check the boxes if you want to
  • "Mount persistent Knoppix-Homedirectory"
  • "Add as persistent, writable system area"
  • "Overwrite/update stored system configuration in image"
  • "Start INIT-bootscripts (network, printer etc.)"

It waits 20 seconds, and if you don't choose "OK" (the default is "Cancel"), it continues booting without mounting the persistent home. Also, it has options 1, 2, and 4 checked by default. Apparently if you don't check off option 3, though, you can't use apt-get (I ended up hanging the system and having to run fsck on "knoppix.img" the first time because I tried to install something but hadn't checked off option 3).

After it mounted the persistent home image, it displayed the message

>> Read-only CD/DVD system successfully merged with read-write /mnt/hda2/knoppix.img.

The image file now contains much more than just /home/knoppix.

You can now use "apt-get update" and "apt-get install <packagename>", etc. as root.

In a word, wow.