Changing a z-visa to a stay type back to a z type again without leaving the country

Hi

I am looking to finish with my current employer (terminate the contract but work the 2 months' notice). They have said that any person who breaks contract must cancel their FEC and change to a stay type. However, I wish to change jobs and stay in China. Can my next employer transfer the stay type to a z type before the stay one expires or do I need to leave the country?

Thanks