Upvote:5
Yes. If you want to stay after your visa expires, you should apply for another visa before your trip (it is not possible to apply for a visa once you're in the Schengen area). If they grant it, it will be valid from 13-11-2016. You will still need to comply with the 90/180 rule, independent of the fact that you have two visas.
The country to which you apply should be the main destination of your trip. The port of entry is not relevant unless your trip doesn't have a single main destination.