Damaged passport

Hi,

I am a British Citizen currently staying in Shenzhen on a multiple entry tourist L (90 days per visit). My passport has become so badly damaged that I cannot leave the country until I get a new one (this will take 6 weeks) and I only have 3 weeks left on my current visa stay. Do you think that the Exit and Entry Bureau would be able to extend my entry permit long enough for me to receive my new passport?
Thanks in advance!

Max