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The schedulability analysis of Controller Area Network (CAN) developed by the research community is able to compute the response times of CAN messages that are queued for transmission periodically or sporadically. However, there are a few high-level protocols for CAN such as CANopen and Hägglunds Controller Area Network (HCAN) that support the transmission of mixed messages as well. A mixed message can be queued for transmission both periodically and sporadically. Thus, it does not exhibit a periodic activation pattern. The existing analysis of CAN does not support the analysis of mixed messages. We extend the existing analysis to compute the response times of mixed messages. The extended analysis is generally applicable to any high level protocol for CAN that uses any combination of periodic, event and mixed (periodic/event) transmission of messages.