<p>With the widespread deployment of multi-constellation satellite navigation systems, the application prospects of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm have become increasingly promising. However, in a multi-constellation environment, the significant increase in the number of satellites leads to a substantial rise in the computational complexity of the ARAIM algorithm. In addition, the ARAIM algorithm is subject to excessive reliance on the Integrity Support Message (ISM). While the ISM parameters are crucial for integrity monitoring, an over-reliance can result in insufficient adaptability across different systems and application scenarios, especially when the satellite constellation and signal environment change. To address these challenges, a flexible ARAIM user algorithm is proposed. Firstly, a satellite-number-constrained flexible ARAIM framework is presented. Then, an intelligent algorithm is employed to establish a mathematical mapping between satellite selection, geometric configuration, and the ISM. This approach enforces constraints on the input satellites to optimize the computational efficiency. Finally, the feasibility of the flexible ARAIM user algorithm is validated using global almanac data and real signal processing. Experimental results show that the proposed algorithm effectively relieves the sensitivity of the ISM parameters while reducing the computational complexity of the conventional ARAIM user algorithm.</p>