Can I get a tourist visa right following a student X type and without leaving the country?

I'm doing an exchange with a chinese University next year and because I'm leaving for a semester, I'm going to apply for a X2 type (student type for less than 6 months). Nevertheless, because my exchange is during the spring semester, I would be interested in staying in China a little bit longer, just to travel around and for touristic purposes. Is it possible to extend my visa? by that, I mean, apply for a touristic L type (of 30 or 60 days) following my student X type and without leaving the country? (I would then go from the uni to that trip around China automatically)