Since your base class doesn't restrict how you access $self, you can just put the extension attributes into an instance of the base class:

package Extended;
sub new {
  my $class = shift;
  my $closure = Base->new;
  $closure->(CELLULAR => undef);
  $closure->(EMAIL    => undef);
  bless $closure, $class;
}
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Why are you using this design? I don't see any advantages to it over more traditional styles. I guess it takes care of generic accessors.