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The Controller Area Network (CAN) is a widely used real-time network in automotive domain. We identify that the existing response-time analysis for messages in CAN with some of the connected nodes implementing priority queues while others implementing FIFO queues does not support the analysis of mixed messages. The existing analysis assumes that a message is queued for transmission either periodically or sporadically. However, a message can also be queued both periodically and sporadically using a mixed transmission mode implemented by several high-level protocols for CAN used in the industry today. We extend the existing analysis which is generally applicable to any high-level protocol for CAN (with priority-and FIFO-queued nodes) that uses periodic, sporadic, and mixed transmission of messages.