Custom install profile calls another install profile
The way install profiles work on Drupal 6, I don't think this will be possible. The modules that are installed are based of the dependency list in the .info file, and since you can't depend on an install profile you can't create that full attachment.

You could come far, by doing includes and callling the fuctions that would otherwise be called by Drupal though, but you would probably have to maintain your own .info file.