Can this be done?

I have a friend who wants to buy another house but can't without help getting a mortgage with someone else (close family member) who has a much better income.

Her house is fully paid off and is solely in her name. She wants to remortgage the house for a deposit to buy another as an investment. Can she get this close family member to remortgage her own fully paid house, jointly as this close family member isn't on the deeds for her house.