The simplest option is to have different test files in your project, each of them using a different configuration that you specify during setup.
A more complex alternative is to have multiple test environments. MIX_ENV=test_foo, MIX_ENV=test_bar and so on. And then specify config/test_foo.exs, config/test_bar.exs and so on. That's what Ecto uses to test multiple adapters/databases. The only issue is that Elixir will compile your project per environment but you can set that to false as build_per_environment: false in your mix.exs.
There are probably many options between those two, it is hard to say which one works better without more details.