In the governance of the shared mobility market of a city or of a metropolitan area, there are two conflicting principles: 1) the healthy competition between multiple platforms, such as between Uber and Lyft in the United States, and 2) economies of network scale, which leads to higher chances for trips to be matched, and thus higher operation efficiency, but which also implies monopoly. The current shared mobility markets, as observed in different cities in the world, are either monopolistic, or largely segmented by multiple platforms, the latter with significant efficiency loss. How to keep the competition between platforms, but to reduce the efficiency loss due to segmentation with new market designs is the focus of this paper. We first propose a theoretical framework of shared mobility market segmentation and then propose four market structure designs thereupon. The framework and four designs are first discussed as an abstract model, without losing generality, thus not constrained to any specific city. High-level perspectives and detailed mechanisms for each proposed market structure are both examined. Then, to assess the real-world performance of these market structure designs, we used a ride-sharing simulator with real-world ride-hailing trip data from New York City to simulate. The proposed market designs can reduce the total vehicle-miles traveled (VMT) by 6% while serving 2.9% more customers with 8.4% fewer total number of trips. In the meantime, customers receive better services with on-average 5.4% shorter waiting time. At the end of the paper, the feasibility of implementation for each proposed market structure is discussed.