That's actually a very demanding requirement. I want my bank to sync all the money they receive to my bank account as well, not just those transaction that specifically has my account number in the destination. But the bank always tell me no.

But it's not impossible depending on what you want to do with the synchronized data. I've spend my whole life selling storage level synchronization for disaster recovery,reporting, etc. (Symmetrix Remote Data Facility SRDF), so you can always buy a good SAN storage to sync data. You can also do it at database level with Postgres data sync to do at database level plus some solution to sync the file store. These solutions are normally 1 to 1 or 1 to many but normally will have a source and some destinations. If the other database is readonly like for point in time reporting purposes to reduce load on production system, a SAN snapshot/mount or automated backup/restore would surface.

If you know coding, you can always override odoo's model to replicate every write to the other database. That way, every write to a database can be replicated on the other and vice versa. But then you'll have to handle all the nuiance of difference record id on different database, or errors when one of them is down etc. But this will be very technical and if you can do it, you wouldn't have asked the question in the first place.