Recent advances in the development of modular transport vehicles allow deploying multi-purpose vehicles, which enable alternate transport of different demand types. In this study, we propose a novel variant of the pickup and delivery problem, the multi-purpose pickup and delivery problem, where multi-purpose vehicles are assigned to serve a multi-commodity flow. We solve a series of use case scenarios using an exact optimization algorithm and an adaptive large neighborhood search algorithm. We compare the performance of a multi-purpose vehicle fleet to a mixed fleet of single-purpose vehicles. Depending on cost parameters, our findings suggest that in certain scenarios, the total costs can be reduced by an average of 13% when multi-purpose vehicles are deployed, while at the same time reducing total vehicle trip duration and total distance traveled by on average 33% and 16%, respectively. The required fleet size can be reduced by 35% on average when operating multi-purpose vehicles. The results can be used by practitioners and policymakers to determine if the combined service of passenger and freight demand flows with multi-purpose vehicles in a given system will yield benefits compared to existing transport operations.