Safety schools for me

<p>From my school in collaboration with RPI, I won a $60K scholarhisp (over 4 years) there provided I get in. I will almost certainly apply there now, and I’ve heard that sometimes you can get other schools to match scholarship money one school is giving (the price). Is that possible? What range of caliber of schools would likely match the price of education at RPI? Is there a chance colleges like MIT or stanford or berkeley would even lower their cost based on negotiating with the cost of RPI? </p>