I agree with Jmat - there could be a very specific situation where "another people" might work, but certainly not in a general sense. "Another people" *is* a horrible mistake because "another" means one, and "people" means many. The words don't go together. I'm also keen to know what the original sentence/context was.

What was the sentence (or at least the context) you heard it in? Is there is a chance you misheard it? Are you sure that person was a native speaker? "Another people" COULD be correct, where 'a people' refers to a cultural group. In this case, the singular is "people" and the plural is "peoples" e.g. "They are are a very proud people". This usage isn't very common though.