This paper investigates a multimodal system that integrates the general dial-a-ride problem with a set of fixed-line vehicles having a flexible schedule. The passenger trips are made in a three-stage journey using a dial-a-ride vehicle and a fixed-line bus. Passengers are picked up from an origin point and transferred to a collecting point via a dial-a-ride vehicle. Then, fixed-route buses transfer passengers to a second collecting point where another dial-a-ride vehicle will pick up and transfer them to their requested destination. The main objective of this integration is to reduce the total trip cost by carrying part of it through cheaper fixed-route service while maximizing the utilization of seats in the fixed-route vehicle. The model provides each fixed line with a suggested start time. A mixed-integer linear programming model was developed for the problem, and computational testing on small-size instances has been carried out to demonstrate the viability of the proposed system.