I have a F visa, 2 entries. Is there a deadline to apply for residence permit?

I arrived in Shanghai on the 28th of August, I have 90 days tu use my second entry. I plan to fly to Korea the first week of october. Can I apply for residence permit (to get more entries) after my trip? Or will it be too late?
I am afraid I have not enough time to apply for residence permit BEFORE my trip, and as I know, my F visa is gonna be cancelled once I get the residence permit, so I don't want to lose my second entry with F visa by changing my visa before flying to Korea.
Thank you!