I have some Python code abstracting the database and the business logic on it. This code is already covered by unit tests but now I need to test this code against different DBs (MySQL, SQLite, etc...)
What is the default pattern for passing the same set of tests with different configurations? My goal is making sure that that abstraction layer works as expected independently of the underlying database. If that could help, I'm using nosetests for running tests but it seems that it lacks the Suite Test concept
Best regards.
Nose supports test suites  just import and use unittest.TestSuite.  In fact nose will happily run any tesys written using the standard lib's unittest module so tesys do not need to be written in the nose style to be discovered by the nose test runner.  
However, I suspect you need morw than test suite support to do the kind of testing you are talking about but more detail about your application is necessary to really address that.
Running the same tests with different configurations