Applying for S2 visa whilst in China on a tourist visa

I am currently on a tourist L type visiting family in Shanghai (my L type expires the 28th of Feb). They both have work visas and I would like to stay longer to take care of their little baby. Is it possible to apply for a S2 type in China or must I exit the country to Hong Kong or Thailand (which is where I got my tourist L type) to apply for the visa?
Side note : I've already been to the Exit and Entry offices and asked for an extention of my tourist L type but they told me "you cannot extend a tourist L type" Thanks for your help.