This paper investigates a drayage problem generalizing a previously proposed, which is motivated by a case study of a real maritime carrier. To serve export and import customer requests in the hinterland of a port, a fleet of trucks able to carry one or two containers of the same size is adopted. The aim of this study is to enlarge the supply of the types of service to fulfill additional needs of the customers by considering two main aspects. As first, there exist overweight and special commodities, i.e. flammable goods, that cannot be carried together with other loads. Secondly, the customers want to choose whether the arriving container is immediately loaded or unloaded (stay-with service) or left at their location (drop & pick service). It is pointed out how the number of feasible routes is affected by the number and type of transportation requests. A Set Partitioning formulation and two scalable heuristics of route selecting are proposed. We present a way to estimate the running time of the algorithms so that the user can choose which algorithm to apply. The experimentation shows that the proposed enlargement of services can be managed to the optimum or with a small error.