Urban mobility solutions such as mobility-on-demand services have become prevalent given the convenience of door-to-door transport. However, a majority of these approaches are user-centric greedy solutions that cause traffic congestion. We propose a near social-optimal routing algorithm which accounts for the overall network traffic congestion. Specifically, we leverage on multi-class mobility options to dissipate traffic congestion while maintaining near social optimal travel time efficiency. We divide each route into three parts with micro-mobility options such as walking or cycling for the first and last parts and on-demand cars for the middle part of the route. In addition, we propose a computational and travel time efficient transit point search algorithm for switching between different modes of travel. We validate our approach by using a diverse set of road networks from different cities. We achieve an average of 84% increase in network utilization by using our proposed multi-class social model compared to single-class user-centric approach. Our proposed transit point search algorithm is on average 68% more computationally efficient with an insignificant maximum average travel time delay of less than 5 seconds compared to an optimal exhaustive routing solution.