The increase in life expectancy has led to a growing demand for adapted transport services for people with reduced mobility. This trend highlights the urgent need to rethink and redesign transport services, both in their structure and accessibility, to enhance the quality of service for this group. Although adapted collective vehicles are available, the saturation of public transport during peak hours significantly diminishes service quality, disproportionately affecting individuals with reduced mobility. High occupancy levels make access and comfort challenging, while the limited availability of adapted collective and discretionary vehicles falls short of meeting the growing demand. This study investigates, through a case study, the potential for shared adapted vehicles to enhance the quality of services provided to individuals with reduced mobility within urban areas. The article analyses a dedicated public transportation program incorporating discretionary vehicles under a co-payment model, financed through a combination of user contributions and local government funding. To assess the feasibility of users sharing vehicles while maintaining service quality, this work uses the route optimization tool, STORK, which readily accommodates the constraints of shared rides, allowing to easily model and analyse various sharing scenarios. STORK enabled us to evaluate the impact of ridesharing on key performance indicators, such as travel time, vehicle utilization, and service coverage.