Can I mix a tiny bit of milk with catfood to coax my cat into eating?

My sister's cat is getting kind of skinny although she does eat and is starting to take some if in small pieces. However, I want her to eat more because she is getting thin. Since she really likes milk (she's only had some when it fell on the floor or when she snuck it from my cereal bowl) I was wondering if I could put a small portion like a few drops or half a teaspoon into her food. I would then add the chicken broth from when I heat it up (warm enough but not too hot, of course) so that she would think it's all milk. Would that work? Or would that just give her a stomach ache and make her sick? I try to stop her from drinking spilled milk but she really likes the stuff and hasn't gotten sick once. It's only happened two or three times though and few and far between. I was just wondering if that would work. Any thoughts?