can I apply for a toruist L visa after work Z type expires?

Hi,
I have been in Beijing for one year, and my working permit is gonna expire in three weeks. I would love to stay here a couple of months to travel and visit China and not leave immediately after the last day of work. What are my options? Can I make a tourist L type after the working permit? How many times can I renew it?

Thanks,
Davide