Actually, it is possible to do that with MC too. Just use another library for ripping.
Since those CDs are not in the online CD database and MC cannot get the appropriate file names from there, you could rename your old files temporally to this structure:
Base folder\Album Artist (auto)\Album\Track #. (The correct track info is preserved in the library fields).
When you rip new files just use a different library, a separate base folder and a similar naming structure like this:
Another Base folder\Album Artist (auto)\Album\Track #
You need to fill only the Artist and Album fields. MC will use track numbers as filenames. If the CD has various artists use (Multiple Artists) as the artist name so you need to write only one artist name.
After you have ripped the files, replace the old files with the new files outside MC.
Inside MC load your standard library, do "Update Tags (from library)" and then "Update Library (from tags)".
After that you can rename the files as you had previously.
Naturally, before doing anything like this you should backup everything (the database and the media files.)