I think it may differ from city to city, but in Shanghai you can extend L visas twice, at 30 days each time (I’m an American and I did this twice last year).
Technically it’s not an extension – they will cancel your original 90 day L visa and issue a new 30 day L visa, which you can then do one more time. After the following 60 day period, you will have to go to HK (or wherever) to get a new visa. This may put a snag in your plans if your current visa is still good for awhile and you don’t want to have to get a new one. As far as I know, there is no way to extend an L visa without cancelling the current one.