If one professor gives recommendation letter to too many students then does it affect the admission of students? I am planning to apply for masters in US universities for fall 2020. I graduated from a school where the staff is quite less. Because of this reason, students tend to ask for recommendation letters from the same professor. When I asked some of the professors for a recommendation letter, they said they are already giving recommendations to 10 to 12 students. Though they don't mind giving a recommendation letter to one more student, will it affect the admission process of the students recommended by the professor? As the professor is already recommending too many students.
I think that is pretty unlikely, as long as the professor is honest in what they say. I'm assuming, of course, that these letters go to various places, not all the same. But, if everyone is applying to the same university and gets the same letter, few will succeed. But that is at least partly because the number of open slots is limited. 

I think this should not be a worry unless the situation is very specialized.