So I read your next post. Seems to me they left a lot of wiggle room. My daughters now 26, so you have an idea how long ago. But we called first to find out possibilities or other merit and had a contact. At smaller schools we found out that certain departments talk to each other. They could actually be in the same building just down the hall. I was visiting and sitting in the same office area for something and actually heard “so and so seems to really want to be here but needs to talk to financial aid /merit to make it happen”. These were Lacs of under 2,000 students.
Then we followed up with emails to the contact person. At a smaller school that contact person can be the head of the department also. But first off I would just be honest about it. All schools understand financial limitations. They want your daughter at their school. If you are 100% set on the one school, they are there to help. I can’t imagine that for $2,000 they will put up much of a road block (not knowing the school this is only a guess). Worst case maybe they will meet you half way?
If that they say “We need to reserve the merit for other students” then just ask how else they can close the gap you need.
She was being sought after by a few schools, and maybe made this easier but what really ended up helping was emailing the head of the department and merit/scholarship department and being upfront about what the needs were and what the other school offered. That closed the deal.
Again, small school it’s easier and have seen this play out several times. Big Uni, not as much.