Answer:
Yes, your bank can make a loan to consolidate and refinance an individual's student loans, but it needs to be aware that the loan will be a private education loan subject to Subpart F of Regulation Z. Accordingly, there are special disclosures that will need to be made, and special procedures that need to be followed.
The loan that your institution would offer may not be the best option for the individual's refinancing needs. Part of the disclosures that you will be required to make will notify the consumer of that fact.