Is this maybe already possible somehow? If so, how is it done?

It would be great to simply be able to overwrite/replace the existing configuration files on the Knoopix CD instead of having to use a separate disk for this, before logging out of Knoppix.

I've burned the Knoppix ISO file on a 700MB CDRW disc and noticed there are approximately 2MB of space left on the disc. That should be more than enough space to replace the configuration disc...