It is well-documented that in Apache, you can restrict access to
particular subdirectories using .htaccess files.  For example, the
following lines in an .htaccess file will restrict access to those
listed in a specific file named "users.txt":

  AuthName "restricted stuff"
  AuthType Basic
  AuthUserFile /usr/local/etc/httpd/users.txt

My question is, can you use multiple "AuthUserFile" lines?  For
example,

  AuthUserFile /usr/local/etc/httpd/basic_membership.txt
  AuthUserFile /usr/local/etc/httpd/premium_membership.txt

To consider this question answered I need to know the specific
versions of Apache that support this feature (if any).

I believe you will find that in all versions of Apache only the last
AuthUserFile entry will be recognised -- but it should be easy enough
to experiment and verify this.