You can't. At least, what you are asking for is not what class inheritance does. It is some sort of run time information sharing and there are lots of ways of doing that depending on what you actually want to achieve. It maybe that a clonish constructor does what you want (but probably not, and there are nasty gotchas):

#!/usr/bin/perl
use strict;
use warnings;

package Top;

sub new {
    my ($class, %params) = @_;
    my $self = bless \%params, $class;

    $self->{var1} = 'Top set var1';
    $self->{var3} = 'Top set var3';
    return $self;
}


sub clonish {
    my ($class, $other, %params) = @_;

    return bless {%$other, %params}, $class;
}


sub doPrint {
    my ($self) = @_;
    my $type = ref $self;
    
    print "Test ($type): $_ => $self->{$_}\n" for keys %$self;
}


package Top::Extend1;

push @Top::Extend1::ISA, 'Top';

sub doPrint {
    my ($self) = @_;
    my $type = ref $self;
    
    print "Override ($type): $_ => $self->{$_}\n" for keys %$self;
}


package Top::Extend2;

push @Top::Extend2::ISA, 'Top';

sub new {
    my ($class, %params) = @_;
    my $self = $class->SUPER::new(%params);
    
    $self->{var1} = 'Top::Extend2 set var1';
    return $self;
}


package main;

my $test = Top->new(passed1 => 'this is copied');
my $one  = Top::Extend1->clonish($test);
my $two  = Top::Extend2->clonish($test, something => 'extra');

$test->doPrint();
$one->doPrint();
$two->doPrint();
[download]

Prints:

Test (Top): var3 => Top set var3
Test (Top): var1 => Top set var1
Test (Top): passed1 => this is copied
Override (Top::Extend1): var3 => Top set var3
Override (Top::Extend1): var1 => Top set var1
Override (Top::Extend1): passed1 => this is copied
Test (Top::Extend2): var3 => Top set var3
Test (Top::Extend2): var1 => Top set var1
Test (Top::Extend2): passed1 => this is copied
Test (Top::Extend2): something => extra
[download]

If you tell us more about the problem domain we may be able to offer a better solution. Quite likely you are trying to use the wrong tool for the problem at hand and the monk's wider experience may be able to give a better approach.

have the result say "this is shared" for each Extra Test

package Top;
# ...
sub shared {
    my ($self) = @_;
    my $type = ref $self;
    print "Test ($type): This is shared\n\n";
}
# ...

package main;
# ...
print "Extra test:\n";
$test->shared();
print "Extra one:\n";
$one->shared();
print "Extra two:\n";
$two->shared();
[download]

Extra test:
Test (Top): This is shared

Extra one:
Test (Top::Extend1): This is shared

Extra two:
Test (Top::Extend2): This is shared
[download]