Temporary Residence Permit extension

Hi. Currently I have a temporary residence permit because I am currently studying here in Shanghai. My RP ends on December 16, but I want to stay in China longer maybe one month or two months because I plan to travel. I heard that one can extend his/her visa for 2 consecutive months (30 days each), can I do this with current X? Or do I have to change to tourist? Please help. Thank you SO much.