Each province interprets and applies the rules in a different manner. Even within a province there may be differences based upon who you are, where you are from, how valuable you are and how valuable your employer is.

This is something your employer should handle, not you. If you go to the local Exit and Entry Bureau you are going to get the standard boiler plate answer.

This forum is NOT the place to seek reliable specific advice on such an important issue. You will only hear personal stories that have absolutely no general application anywhere.

Not completely true Martin, I have been a legal advisor for 3 years in China.
The answer to your question bengalsky is how ever answered correctly by Martin. The easiest way is to let your company do this. Keep in mind if the foreign company pays you in foreign currency then only your business visa needs to be extended. If you are staying in China long term and are going to be paid in RMB then the Z visa will be needed. There are agencies who can assist with this process but they will lie about you not having to leave China for your first Z visa. If you are located in Shenzhen, Beijing, Shanghai, or Tianjin, you will be required to exit to your home country for your first visa. After that, you can renew in your working city annually.
If you can go to Honk Kong please note that all expediting services have been stopped and the visa generally takes 3 to 5 days. If you have to exit China to your home country, not to worry, for 20 US dollars, you can get your Z visa in 2 hours, at the most one working day. You can be on a plane back to China in no time. Do your physical check before you leave at your local exit and entry hospital. It's cheaper and less personal. Not only that, even if you receive one from your country, they would request it to be redone at one of their expat hospitals. I hope this helps.