Calling about merit award with comparable scholarship

My son has received a nice scholarship offer from a large state U and we are waiting on the information for his 1st choice. These two schools are extremely similar in ranking, culture etc. has anyone ever called to see if a school will increase a merit award based on what their child got from a very comparable school? If so, what was the process and how did it go?

We did with our oldest son. In his major, there are about 5 schools that are always the top 5 in rank. His first choice school is usually ranked #1 or #2, and had offered him a nice package. The other school that is usually either #1 or #2 did not offer him anything, but the next 3 schools offered nearly full rides. We took the offers from the 3 schools to a meeting at his first choice school, and they did increase his offer. Our son told the guy we were meeting with that he really wanted to attend that school, but he was having a difficult time deciding because he had these other offers, and then he just asked if they might consider increasing his offer. Later, when my son got even more offered from one of the other schools, he emailed his first choice school (same guy we had met with already) but the guy emailed him back and said they could not offer any more. Our son ended up going there, and actually did end up with more money by the time his freshman year started. I think it is significant that the schools are similar in ranking, as you mentioned. Good luck!