Ask HN: How to deal with multi-tenant SaaS database structure?

Hello HN, I'm building a SaaS product. Each tenant can have their own database structure/fields while many tables are common between the tenants. For example table A is common for all of them while table B might have different fields upon organization/tenant's need, in other words we have table B for all orgs with different fields.

I'm thinking of shared-codebase and shared-database paradigm for it's simplicity(no synchronization needed). Have you encountered this situation? Is it possible/and how to handle this objective with single database for all tenants? Further, I'm using PostgreSQL database.

Thanks in advance.