There's no limit to the number of scholarships a student can apply for or receive.
One common misperception is that if a student gets an outside scholarship (that is, a scholarship from a private organization), this can be a bad thing because it will lessen the amount of aid the student can get from the college and from federal and state sources.
The fact is that if the total aid your child receives ends up being a certain amount over their calculated need, federal law requires that the college reduce the need-based aid it offers your child. But that doesn't mean your child will have to pay a bigger share of their college costs. It just means that the scholarship dollars replace financial-aid-package dollars.