Will applying for multiple master programs in the same department improve or worsen my chances of getting admitted to my preferred program?
Speaking as someone who did apply to his own undergraduate institution for a graduate program, and as someone whos institution has two programs within the same department (although I did not apply to both). I don't think it will have a big impact on your chances of getting accepted into a single program, here is why I say this.

At my institution they have different people reviewing the applications into each program, meaning it is likely at your institution the same person will not see nor know that you applied to another program as well.
I was actually advised to apply to both, though I did not apply to both.

As others have mentioned, you can ask around and get a final confirmation from someone at your institution on how they feel about you doing this.