It would be cool to be able to call this new method in my program via the base class

That's what subclassing does: you can call any method from the base-class, and if the subclass implements or overrides that method, the subclass's method will be called.

package Base;
sub method1 {
  my $self = shift;
  $self->method2();
}

sub method2 {
  print "Base\n";
}
package Sub;
@ISA = qw(Base);

sub method2 {
 print "Sub\n";
}

package main;
Base->method1;
Sub->method1;
__END__
Base
Sub
[download]