I think I probably submitted a total of 8 letters to almost every med school. Since I had a previous career, I was told that it is wise to usually have a LOR from every point in your life as to give a sense of how your progressed through your schooling and career as well. As long as you're not collecting LOR's for the sake of adding LOR's and that each LOR you can reasonably assume is going to be strong, it should be ok.
Edit: I should note that almost all the letters were contained within my premed committee packet, and I didn't just add each individually to AMCAS