Yes, some colleges allow limited stacking where an outside scholarship first replaces student loan and/or work expectation and unmet need (if any) before reducing need-based financial aid grants.
https://financialaid.stanford.edu/aid/outside/
https://fas.ucsd.edu/types/scholarships/index.html (scroll down to “FACTS ABOUT SCHOLARSHIPS”)
However, if the college reduces grants first, then there is no advantage to getting an outside scholarship, unless the student transfers and can take the scholarship to the next college where it can replace something other than grants there.