I had the same experience and while I don't know how you can fix your current problem it is possible to install to multiple partitions during the install.

Make your own partitions
Format the partitions
sudo knoppix-installer
Configure installation. (You will have to let the installer choose a large partition until you edit .knofig)
Quit the installer
Save your configuration
sudo mcedit .knofig
*NOTE* .knofig will be found in the directory it was launched from. Use updatedb and locate .knofig if you can't find it.
Edit the "HD_MAP=" line and add your preformatted partitions for example:

HD_MAP="/dev/hda3:/home /dev/hda6:/tmp /dev/hda7:/var /dev/hda14:/usr"

*DO NOT try to move /boot to its own partition. It won't work.

HD_IGNORECHECK="yes"
*Setting HD_IGNORECHECK allows us to install / to a smaller partition.

HD_CHOICE="/dev/hda1"
*HD_CHOICE to select a different partition for /

Save it and relaunch the installer. You DO NOT need to "Load saved configuration" as it will automatically find .knofig. After starting the installation, open another terminal window and issue mount and you should see your partitions mounted for installation.

This has worked for me many many times. If it doesn't work please retrace your steps. It's easy to have a small error in the steps.

HTH