Approximate computing emerges as an energy-efficient computing paradigm designed for applications that can tolerate errors. Many iterative methods for approximate logic synthesis (ALS) have been developed to automatically synthesize approximate circuits. Nonetheless, most of them overlook the potential of applying multiple local approximate changes (LACs) simultaneously in one iteration, which can significantly reduce the overall computation time. In this article, we propose AccALS 2.0, a novel framework for further accelerating iterative ALS flows, which is based on simultaneous selection of multiple LACs in a single round. However, there are two challenges for selecting multiple LACs. The first is that the mutual influence of multiple LACs can affect the estimation of the circuit error. The second is that there may exist conflicts among multiple LACs. To address these issues, first, we propose an efficient measure for the mutual influence between two LACs. With its help, we transform the problems of solving the LAC conflicts and selecting multiple LACs into a unified maximum independent set problem for solving. The experimental results showed that AccALS 2.0 outperforms state-of-the-art ALS methods in runtime, while achieving similar or better-circuit quality.