I have two research mentors who are in the process of writing recommendations for me. For schools that only allow one additional rec (aka Other Recommender), I will obviously only submit one.
However, for schools that allow for two, would it will be overkill to send in two? Yes, they might cover similar ground, but I have equal confidence in both letters to be outstanding and much stronger than my two teacher recs. I don’t mind if the AO only reads one of them, or if he/she only has time to skim both letters. I just feel that having 2 will confirm and give greater credibility to the qualities that they describe in their respective letters.
Given the stigma on sending too many recs, would sending 2 recs annoy the AOs and make them a bit “turned off” towards my app? Or will they understand my choice, if both letters turn out to be very strong (hopefully)?
Remember that any “optional” material might be skimmed. Unless your additional recommender truly knows you as a person and could testify to something that your teachers can’t, I would not recommend sending them to the school (if you absolutely feel your teachers will not display your character in a “wow” way, submit one). Yale, for example, says that sometimes “less is more.”
Don’t do it, it will just annoy them and they probably won’t read the extra one. Get the references and send the best one, if you must, but that kind of isn’t fair to,the person who went out of his way to write it.
If OP waives right to see recs (which I would suggest), s/he won’t know which is better.
Regardless, I agree with the above - less is more. In many cases, the thicker the file, the thicker the kid. More materials to read does not mean that an AO will spin extra time on your app; it just means the some other part will be skimmed.