Online Social Networks (OSNs) are increasingly exploited for campaigns involving the spread of multiple rumors to influence opinions about products or individuals, making rumor mitigation a critical challenge. Unlike existing works that primarily address single rumor scenarios, this research tackles the complexities of multi-rumor influence, where prior exposure can bias users and impact communities unevenly. To address this, we propose a novel Bayesian Inference based Community Influence model that accounts for the community structure of OSNs in assessing the impact of multiple rumors. Furthermore, we introduce a Two-phase Community based Genetic (TCG) algorithm designed to strategically select seed users for counter-rumor dissemination, aiming to effectively mitigate the spread of influence in this multi-rumor context under a given budget. The effectiveness of our proposed approach is evaluated through extensive experimentation on two datasets by considering the budget k.