Yes! you still can have private number plates. But that is possible in NWFP (Pukhtoonkhwa) only.
At first place you have to get a Peshawar number plate and on top of that you can have any number of your choice provided that number is not in use of anyone else. If you have any connections there, ask someone for the exact cost and am sure that getting your car registered there is much cheaper than Lahore as you don't have to pay the luxury tax, which is killing most of the time.