YES!

You can create as many fields for a user as you like. You can even make the fields required, to ensure you capture that information. To create a custom field you will need to be logged in as an admin. Then go to Users and then Manage Custom Fields. There you can create/edit the custom fields. You can setup custom fields to be checkboxes, dropdowns or just text boxes. You can even restrict them for admins only.

 

Custom fields for Admin Only will only be allowed to be viewed/updated by admins.