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I posted this in the middle of another thread so it kind of got lost. If I am sending an LOCI to a school I have been wait-listed at. Could it hurt to send a new LOR? The LOR would come from a partner at a major firm who I have known for a long time. I know she would be able to write me a good recommendation, I'm just wondering if this is the sort of thing adcoms like, dislike, or don't care. Thanks.

I think you should- you have nothing to lose! The only reason for not sending it would be if you've already met the school's maximum number of LORs.