The mobile cellular systems are expected to support multiple services with guaranteed Quality of Service(QoS). But, the ability of wireless systems to accommodate expected growth of traffic load and broadband services is limited by available radio frequency spectrum. Call Admission Control (CAC) is one of the resource management functions, which regulates network access to ensure QoS provisioning. However, the decision for CAC is very challenging issue due to user mobility, limited radio spectrum, and multimedia traffic characteristics. In our previous work, we proposed a fuzzy-based CAC system by considering the priority of the on-going connections. As priority parameter, we considered only one parameter (service request). In this work, we extend our work by adding different priorities. We call this system FACS-MP. We evaluate by simulations the performance of the proposed system. From the simulations results, we conclude that the FACS-MP can differentiate better different services compared with previous system.