I want to open a new iCloud on my iPhone 6s

Marking your own post as Solved may prevent others from trying to help because they think you have fixed your problem.

Create a new ID (if necessary) and sign into iCloud using the same Apple ID on another Apple device/computer. You should then be able to sign in.

The maximum number of free accounts have been activated

Apple ID - create a new.      

Apple ID – Create        

Apple ID - Could Not Create or Could Not Set Up iCloud message.    

Or contact Apple ID Support.  See the Apple Support articles below for contact information.  

Apple ID - Official Apple Support.    

Contact Apple for help with Apple ID account security - Apple Support.   (Link doesn’t always load)  

Get Support          Work through the screens to get a chat option. You may have to pick a slightly different problem.

Apple Support schedule phone call

https://twitter.com/AppleSupport.          People have posted it may take an hour or more to get a response.