I am currently applying for a Ph.D. in Physics in the US. One of my recommenders has already submitted a letter to the schools I'm applying to, but I was advised by another faculty member that I should have gotten a letter from a different professor I worked with since the submitted one wouldn't be as strong. The latter professor would most likely write a stronger recommendation.
All of the programs I'm applying for require three letters, and most allow for four; would simply adding the extra recommender be sufficient or should I contact the school to remove the weaker letter entirely if possible? In other words, would having it there bring down my application if there is a stronger one I could replace it with or would it reasonable to assume that reviewers would consider all four and think of the weaker one as extraneous (since I cannot define a ranked order)?