I'm not sure that I like this solution (I'm pretty sure I don't), but it works (and I now see that this probably is insufficient for what you want in methods that return objects in different classes):

#!/usr/bin/perl

package MyClass;

use strict;
use warnings;

use Want;

sub new {
  my $class = shift;
  return bless {last_op => ''}, $class;
}

sub this {
  my $self = shift;
  if (@_) {
    $self->{this} = $_[0];
  }
  if ( my $op = $self->{last_op} ) {
    $self->$op($self->{this});
  } else {
    $self->{curr_value} = $self->{this};
  }

  return want(qw(SCALAR REF)) ? $self : $self->{curr_value};
}

sub that {
  my $self = shift;
  if (@_) {
    $self->{that} = $_[0];
  }
  if ( my $op = $self->{last_op} ) {
    $self->$op($self->{that});
  } else {
    $self->{curr_value} = $self->{that};
  }

  return want(qw(SCALAR REF)) ? $self : $self->{curr_value};
}

sub andand {
  my $self = shift;
  $self->{last_op} = '_andand';
  return $self;
}

sub _andand {
  my ($self, $value) = @_;
  $self->{last_op} = '';
  $self->{curr_value} = $self->{curr_value} && $value;
}

package main;

use strict;
use warnings;

my $foo = MyClass->new();
$foo->this(0);
$foo->that(5);

print "This: ", $foo->this(), "\n";
print "That: ", $foo->that(), "\n";

my $value = $foo->this()->andand->that();
print "V: $value\n";
$value = $foo->that()->andand->this();
print "V: $value\n";

$foo->this(3);
$value = $foo->this()->andand->that();
print "V: $value\n";
$value = $foo->that()->andand->this();
print "V: $value\n";
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