In at least some embodiments, a processor core executes a sending thread including a first push instruction and a second push instruction subsequent to the first push instruction in a program order. Each of the first and second push instructions requests that a respective message payload be pushed to a mailbox of a receiving thread. In response to executing the first and second push instructions, the processor core transmits respective first and second co-processor requests to a switch in the data processing system via an interconnect fabric of the data processing system. The processor core transmits the second co-processor request to the switch without regard to acceptance of the first co-processor request by the switch.