One option would be a simplistic factory that held a single "shared thing", and was responsible for creating the other objects, so that they could have a reference to the shared thing without having to explicitly pass the "shared thing" around.

Something like this:

#!/usr/bin/perl -w
use strict;
package SharedThing;
sub new {
    my $that  = shift;
    my $class = ref($that) || $that;
    return bless {"counter" => 0}, ref($that) || $that;
}
sub hello {
   my $this=shift;
   $this->{counter}++;
   printf "hello, count is [%d]\n",$this->{counter};
}

package MyFactory;
sub new {
    my $that  = shift;
    my $class = ref($that) || $that;
    my $this = {};
    bless $this, $class;
    $this->{sharedthing}=SharedThing->new();
    return $this;
}
sub A {A->new(@_);}
sub B {B->new(@_);}

package A;
sub new {
   my $that  = shift;
   my $class = ref($that) || $that;
   my $this = {};
   bless $this, $class;
   $this->{factory}=shift;
   # call the "hello" method of the "shared thing" so that
   # we can see that it's indeed a single instance
   $this->{factory}->{sharedthing}->hello();
   return $this;
}

package B;
our @ISA=qw(A);

package main;
my $factory=MyFactory->new();
my $a1=$factory->A();
my $a2=$factory->A();
my $b1=$factory->B();
my $b2=$factory->B();
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All of the instances of A and B have a reference to the factory passed to them when they are instantiated, and so, they can get to $this->{factory}->{sharedthing}...the single shared object.