And one for the road-

BEGIN { # External package in real practice.
    package MyCGI;
    use parent "CGI";
    sub new {
        my $self = +shift->SUPER::new(@_);
        $self->param(OH => "HAI");
        $self;
    }

    sub DESTROY {
        my $self = shift;
        warn "doing my own thing now...";
        warn "parental destruction next...";
        $self->SUPER::DESTROY;
    }
}

# use MyCGI; <-- If in another/real package file.
use strict;
use warnings;
use Data::Dumper;
print Dumper( MyCGI->new );

__END__
$VAR1 = bless( {
                 '.parameters' => [
                                    'OH'
                                  ],
                 'use_tempfile' => 1,
                 '.charset' => 'ISO-8859-1',
                 '.fieldnames' => {},
                 'param' => {
                              'OH' => [
                                        'HAI'
                                      ]
                            },
                 'escape' => 1
               }, 'MyCGI' );
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(Update: added DESTROY. Not quite sure it's the way to go but I am sure someone will chime in if it's not a good idea or quite right.