This paper introduces the Double Travelling Salesman Problem with Multiple Stacks and presents a three different metaheuristic approaches to its solution. The Double Travelling Salesman Problem with Multiple Stacks is concerned with finding the shortest route performing pickups and deliveries in two separated networks (one for pickups and one for deliveries). Repacking is not allowed, but the items can be packed in several rows in the container, such that each row can be considered a LIFO stack, but no mutual constraints exist between the rows. Two different neighbourhood structures are developed for the problem and used with each of the heuristics. Finally some computational results are given along with lower bounds on the objective value.