If what you mean by extending the visa is requesting another 30 days stay at PSB, the answer is no.  Maximum number of extensions are two per stay.

If you have available entries left, just go to Hong Kong and re enter China, and you will get another stay.

with a L visa, 2 times extension is the maximum now. no matter in shanghai or Beijing! want to stay longer?  make conversion to other long duration visa before you current visa expire or go out of China to obtain a new visa come back. like HK .