In the pickup and delivery problem (PDP) a fleet of capacitated vehicles must be routed in order to satisfy a set of customer requests. In this article, we address a variant of the one-to-one PDP where each customer location can be visited several times and load may be transshipped from one vehicle to another at specific locations. The goal is to minimize the sum of travel costs and transshipment costs. The corresponding problem is called the PDP with time windows, split loads and transshipments. We present an arc-based mixed-integer formulation for the problem and propose a large neighbourhood search metaheuristic for solving it. Extensive computational experiments using both benchmark instances from the literature and instances based on real-world data illustrate the performance of the solution method and give insights regarding the benefits of combining split loads and transshipments.