Integration testing multiple Databases for same Tests

[TheMatrixPill]

I have a Project wich should support two Databases using Ef core.

Is it possible to run the same Tests for different Databases?

I am currently using the ClassDataSource<T>(Shared = PerTestSession) Attribute to provide an TestContianer Database to the Baseclass of the tests.
Is there a way to run the tests also with a different Db (parallel or not, trying to use the Attribute a second time does not work.