package Class2;
our $pckg_vars = __PACKAGE__;
sub new(){
  my $class=$_[0];
  my $s = "Base"->new(params)....
  my $s->{$pckg_vars} = {};       #'local' class var space
  bless $s,$class;
  return $s;
...}
package Class3;
our $pckg_vars => __PACKAGE__;
sub new(){
   my $class=shift;
   my $s = Class2->new(params)...
   my $s->{$pckg_vars} = {};       #class3 local vars
   bless $s,$class;
   return $s;
....}
<etc>