Ride-sharing services operated by transportation network companies (TNCs) have the potential to expand capacity and accommodate increasing urban mobility demands, presenting an alternative to traditional ride-hailing services. This study introduces a high-capacity ride-sharing (HCRS) system that leverages user-specific travel choices and incentive-based pricing schemes. This innovative system enhances the dynamic matching problem of HCRS by incorporating a nested choice model and dynamic fare adjustment strategies to boost profitability while encouraging shared travel behaviours. Additionally, a rolling horizon solution approach is employed, including a shared choice set generation algorithm for creating shared alternatives and an Adaptive Large Neighborhood Search (ALNS)-based method for optimal matching. By leveraging a real dataset from Beijing's ride-hailing services, this research underscores that the HCRS service can significantly improve system efficiency and service quality, achieving more than 10.44% reduction in operating costs, and reducing average fares (¥3.31) and emissions (3.49 kg) across various users, compared to traditional ride-hailing services. The findings also demonstrate that users' decision-making is profoundly affected by changes in incentives, highlighting the importance of incentive settings in enhancing user engagement and system performance.