Is it a good idea to get my third letter of recommendation from my summer internship?
If it’s an optional 3rd rec I would only do it if it’s someone/somewhere very impressive AND the letter is very specific about the work you did. If you worked somewhere cool but just licked envelopes all summer just listing it somewhere in your app would be a better bet.
Optional 3d recs should be send in only when they provide information about you that isn’t likely to be provided by the teacher recs. Otherwise it’s redundant.
Agree with the other comments. Only send if if it will be a very enthusiastic recommendation that can speak to something that an academic teacher can’t also comment on on.