Hi I'm a student now in Beijing on a F Visa and I want to extend it.

I graduate this July and my visa is only good up till August (date of entry Febuary 3- I have 180 days) . but I wish to stay in China at least till December in order to travel and practice my Chinese. I do not wish to enroll in another semester with any institute , rather I find a private teacher and study on my own. I also want to rent a new apartment and keep on living in Beijing at least until the beginning of 2013.
my university says they can only give me a 3 month extension on the cost of 2000 RMB which is useless in any way.
can I get a new Visa for half a year? should I apply for a different kind of Visa? if so which one? please let me know how could I stay in china for at least more 6 month without having problems.
Thank you