The maximum number of three accounts have been activated on this iPhone
Presumably to limit account farming, Apple makes it trivial to establish three new accounts on each iOS device or Mac. Since this is detected on Apple’s server side, you can create a new Apple ID from this page (on a desktop computer) or perhaps another device that hasn’t exhausted it’s three. 

Once you have set up your new Account, log in on your iPhone with that ID (Settings > iCloud > enter the new ID) rather than creating it on-device.