Is it too late to ask my teachers for another rec?

So I'm applying to college, and I think there is another college I want to apply to that was not originally on my list. I already have two teachers that wrote the rest of my recommendation letters, but is it too late to ask them to do one more? They would have to finish by January 1st, and my school's official deadline finalize college application lists was 3 weeks ago. Should I ask my counselor if I can apply for one more, or just let that one go?