Extending L type for an extra 10 days in Beijing

Hi there,
This summer I am planning on spending 70 days in Beijing to visit friends (I used to live in China under my mom's job, but I no longer have family there and I don't have a residence permit).
I am going to apply for an L type for 60 days, being invited by permanent residents. I was wondering if it'll be possible to extend my visa for an extra 10 days at the end of the trip while still in Beijing? I can provide invitation letters by permanent residents. I am aware that I'll probably have to leave the country, like go to Hong Kong for a weekend, which is fine.