So in short you want to have a partly shared and a partly private schema and the database should provide the means to figure out when to use which.
There is no technical feature to support this (actually I don't know any DBMS that would have something like this).
Generally speaking, the schema of a SQL database is rather static and cannot be determined based on a session. Sure, you might re-direct data access e.g. via views and synonyms, but object compilation resolves those upon compile time.If the structure changes afterwards, the objects and queries will become invalid.
Your question actually states how to implement your solution to the problem, rather then the problem itself. Maybe there is something we can propose when you share what you actually want to achieve.