May not be applicable to the OP, but Columbia claims to “meet need” for frosh and most transfers, but does not do so for Combined Plan (3+2 engineering with Columbia as the “2” school) transfers.
https://cc-seas.financialaid.columbia.edu/how/aid/works
https://undergrad.admissions.columbia.edu/apply/transfer
https://undergrad.admissions.columbia.edu/apply/combined-plan