From Resident Permit(X1) to Work Visa

Hi! I just finished my language program at an uni in shanghai and will begin my MBA at other uni. My resident permit expires by the end of this month. I will be able to get 2yrs long X1 after I register this September. However, I have a summer job here in Shanghai and don't want to go back to my country just to get a L type. My question is; is there any way I can extend it just until the registration date in Sep? If there is a way to do so, what do I need to get from my employer for the summer job or the uni that I will attend to? Thank you in advance!!