This is possible in supabase. You can store all the data in a table and restrict access with Row Level Security

You also have various ways to separate the data for indexes/performance

- use metadata filtering first (eg: filter by customer ID prior to running a semantic search). This is fast in postgres since its a relational DB

- pgvector supports partial indexes - create one per customer based on a customer ID column

- use table partitions

- use Foreign Data Wrappers (more involved but scales horizontally)