Hm, without more details on the use case and assuming no "round trip to a network" means everything is running on a single host I see a couple of options:

1) Shared memory - use a cache/key-value lib which allows you to swap the backend to some shmem implementation

2) File-system based - managing concurrent writes is the challenge here, maybe best to use something battle tested (sqlite was mentioned in a sibling)

3) Local sockets - not strictly "no network", but at least no inter-node communication. Start valkey/redis and talk to it via local socket?

Would be interested in the actual use case though, if the monolith is written in anything even slightly modern the language/runtime should give you primitives to parallelize over cores without worrying about something like this at all... And when it comes to horizontal scaling with multiple nodes there is no avoiding networking anyway.