You must rewire the single plug socket if you are to change it to a double plug socket. Just get a double surface back box and then fix the wiring as shown in the diagram. If you familiar with the wiring process, it is best if you called an electrician to help you out.
I would definitely hire a licensed electrician to do the work... having faulty outlets can be very dangerous. Try going to Servicerunner.com to source a good person to do the work for you. best of luck!