As @ucbalumnus noted, some colleges do stack.
For example, Yale will first apply outside scholarships to reducing or eliminating the expected student term time and summer earnings contribution. Additional outside scholarship funds above the amounts needed to replace the student contribution can also go towards the purchase of a computer. At Yale, the student contribution is about $6000/year, so up to approximately $24,000 in outside scholarships would “stack” before any reductions in Yale institutional support.
As @twoinanddone noted, some outside scholarship awards (notably the high dollar value major science awards like Regeneron, Intel, Siemens, etc.) permit delaying disbursement until grad school and allow the student to specify the amount of scholarship disbursed from their account each year.
If for example, a student won a $50,000 scholarship they could direct $6,000/year for four years to replace their undergrad student contribution, and then “save” the remaining $26,000 for grad school.