This paper studies the Hierarchical Multi-Switch Multi-Echelon VRP (HMSME-VRP), a newly introduced VRP variant based on a real-world case involving High Capacity Vehicles (HCV). The problem originates from the policies of a distribution company in the Nordic countries where HCVs of up to 34.5 m and up to 76 tons are allowed. The HMSME-VRP offer a new way to model distribution problems to cover large geographical areas without substantial costs in infrastructure. Furthermore, it adds complexity to the standard VRP and, as such, remains NP-hard and difficult to solve to optimality. Indeed, it has been demonstrated that only very small instances can be solved to optimality by a commercial solver. Thus, in order to handle instances of real-world size, we propose two General Variable Neighborhood Search (GVNS) procedures, the second of which is adaptive, utilizing an intelligent reordering mechanism. In order to evaluate the proposed procedures, 48 benchmark instances of various sizes and characteristics are generated and made publicly available, comprising of clustered, random, and semi-clustered customers. The computational results show that both GVNS procedures outperform the exact solver. Additionally, the adaptive version outperforms the conventional version based on both average and best solutions. Furthermore, we present a statistical analysis to verify the superiority of the adaptive version.