The overloaded transportation networks in big modern cities have always been a severe issue, resulting in congestion, environmental pollution, waste of energy, and of people's time and money. In this paper, we will discuss the potential solutions that could be offered by the utilization of a flexible ridesharing system. We will discuss the current standings of existing ridesharing tools and then propose a new flexible ridesharing system that is specifically designed to meet users' time constraints and to increase user satisfaction when there are dynamic road conditions such as traffic incidents. The proposed system is robust in user and traffic flexibility through the use of two main components: Transferring and incentive protocols. We will discuss the necessity for the dynamic road network adaptation and the probabilistic stable routing model, and how they impact the two main components. For final remarks, we will also discuss the challenges of deploying such system into an intelligent transportation system, which includes keeping humans (users) in the loop and adapting to the self-driving technologies.