How to change jest.mock value for different tests when mocked class is a dependency on on the SUT?

Question

I am testing a class DogService.ts. But DogService has a private dependency called CatService that gets new'ed up in the constructor. I can successfully mock the dependency using:

jest.mock('../CatService', () => {
    return {
        CatService: jest.fn().mockImplementation(() => {
            return {
                someFunction: (async (someArg) => {
                    return await someAsyncMethod();
                })
            }
        })
    }
});

And it gets injected fine in the test:

describe("", () => {
    it("", async () => {
        const dogService = new DogService();
        ...
    });
});

There's no import for the CatService in my jest test file. The mock I guess is the import. However, I want to swap out the implementation of CatService in different tests. I have tried jest.resetModules() and a bunch of other things. Further, the above only seems to work when the mock is outside any tests. If I move it into the describe() function the real CatService is used.

Any ideas how to do this? Most tutorials are for mocking classes or functions you directly use in the jest test, but obviously I am mocking a dependency.