From HW point of view MPC5777C implements SEMA4 unit to support multi-core operation. You can find it in reference manual Chapter 13 - Semaphores (SEMA4). Furthermore there are MMU and MPU unit implemented.
Semaphore example you may find for instance here:
https://community.nxp.com/t5/MPC5xxx-Knowledge-Base/MPC5-software-example-list/ta-p/1102445
From SW point of view - AutoSAR OS should provide functions for communication between cores (Inter-OS-Application Communicator - IOC). Potentially third party OS could offer such functionality as well.
Just noting that for newest devices there is separate IPCF package, but it was not available for MPC57xx devices:
https://www.nxp.com/design/software/automotive-software-and-tools/inter-platform-communication-frame...
