Notaniowan, if Allegheny has not already included Stafford loans in your package, as Mom2collegekids says, you will only be permitted to borrow $5500 on your own. Your parents might as well borrow money elsewhere like through PLUS or home equity and pay up the difference and do a separate loan deal with your for the amounts, as having them cosign puts them just as much on the hook for the amounts, and just gives the loan company 2 people to hit for the amounts. Even if one of you passes away, the other is responsible for the payments. If one of you is out of a job or has no money, it can hit up the other. PRetty good deal. So basically, it comes down to whether your parents want to borrow to pay for the difference between Allegheny and Denison.
Personally, I think you are being selfish and putting a lot of pressure on your parents. I'm glad my kids did not do this to us because, it really hurts when your kid wants something. Too many parents will do themselves damage to give the kid what he wants because, we parents love our kids. So do keep that in mind. I could see some of the quandry if the schools were so different like East New Mexico State vs Allegheny, but Denison vs Allegheny? GIve me a break, please. I know both schools, and they are similar enough and close enough that the difference in cost for them would make the deal for me in an instant.
I would give Allegheny a call and ask if there is any possible way that they can bridge the gap more closely and if they cannot, I would not ask my parents to borrow to make up that difference. It isn't worth it.