The classic dial-a-ride problem (DARP) aims at designing the minimum-cost routing that accommodates all requests under a set of constraints. However, several modeling and computational challenges have hindered the successful deployment of dial-a-ride solutions. This work proposes incorporating user preference decisions within a rich DARP formulation. Specifically, it is considered that two travel modes are available: a shared mobility (DARP) service and a private travel option. Utility functions for each travel mode are integrated and it is assumed that the utility of the shared mobility service depends on the collective choice of travelers whereas the utility of private travel is fixed. Assuming that travelers are rational and seek to maximize their trip utility, extra variables and constraints are added to ensure that all requests are served by the mode with the higher utility. The behavior of the proposed integrated DARP with formulation of user preference constraints is examined by comparing the optimal solutions and computational time of this model with its classic DARP counterpart. Furthermore, the impact of various formulations of fare and the tolerance of the integrated DARP model is explored. Results show that user-personalized fare formulation improves model tolerance and profit margin, albeit it is rather computationally expensive.