With the new surveys in Freshdesk, you would be able to set up an additional set of questions that you could send out to the customers. 

Please navigate to Admin -> Workflows  -> Customer satisfaction -> click on edit next to the survey to be taken to the survey details. Below the thank you page, there is an additional questions section that could be set up and sent out to the customer.

If you are on the Estate plan or higher, drop a quick email to support@freshdesk.com to have this enabled for your account.