Applying for a tourist visa while already in China?

I am currently in China on a legal Z type. It will expire in a month, and I don't want to renew it. However, I would like to spend a month traveling in China before returning home. Is it possible to apply for a L type to have an additional month of travel in China before my current Z expires, or will I have to return home to apply? (In that case, it's not worth it) Thanks.