Can I reapply for a new Z visa even if I still have a valid residence permit?

Hi,

I have a residence permit still valid until next month, I transferred to a new employer and I got all the documents needed for me to reapply a Z type in my home country. I am just not sure if the consulate in my home country will accept and issue a new Z type for me as I still have a residence permit. Do I need to have it cancelled first before I can apply for a new Z type from another employer? I wish you could help me with this.

Also, I have resigned and got a new employer now, I haven't started my new job yet as I waited for my new work permit and the documents from my new employer. I did not go home as they told that there is no need for me to exit China, so I stayed and waited for all the documents. Unfortunately, after I got all the necessary documents, the person in charge of my Z type told me that because each city in PRC has different policies, so I need to go home and apply a new Z type in my country instead of just transferring my residence permit in PRC. Is my stay here considered illegal, even though I am not working yet?

I hope you can give me some advice regarding my concerns. Thank you!

Thanks,
Trish