It's hard to suggest an optimal solution without knowing what the methods are doing, how they are constructed, etc. But here are a couple random thoughts to consider:
One possibility might be to break the method up into two or more methods, isolating the part that will be different into its own method (probably private). Then you would only need to overwrite that "sub-method". In the most extreme case, that private method might be empty in the Visitor class, with the main method calling it even though nothing will happen.
Another possibility might be to overwrite the method, but the bulk of it would duplicate the parent method simply by invoking it:
class User extends Visitor
{
public function example()
{
parent::example();
// additional code here...
}
}