package Parent;
sub X {
   my $self = shift @_;
   print "called Parent::X()\n";
   ...
}
# -------------------
# and in the Child class you specialise this
package Child;
use base qw(Parent)
sub X {
   my $self = shift @_;
   $self->SUPER::X(@_); # Call Base class method

   # local function NOT inherited
   _X($self,@_);

   ...
}
sub _X {
  my $self = shift;
  print "called Child::_X()\n";
}
# -------------------
# and further down the chain...
package GrandChild;
use base qw(Child)
sub X {
   my $self = shift @_;
   $self->SUPER::X(@_); # Call up one level
   # then do some extra grandchild stuff

   # local function NOT inherited
   _X($self,@_);
   ...
}
sub _X {
  my $self = shift;
  print "called GrandChild::X()\n";
}