Just in case it still helps anyone: Our son wrote a heartfelt letter (not us parents) to the Dean of Admissions, copied to his AO, at a school where he’d already gotten good merit and a need-based grant, but we still needed a little more. He felt a deep connection with this school, and he really communicated that in his letter. He referred to one other school’s offer, but not in a way that you’d call a negotiation. He received a significant increase in a renewable scholarship. Your mileage will vary. 
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