It sounds like your Mac has reached the limit of how many iCloud accounts it can create. To explain what's going on, I need to start with a bit of background about the Apple ID/iCloud account system.
An Apple ID is basically an identity in Apple's system that you can use to interact with Apple for a wide variety of services -- iCloud, iTunes music purchases, App store purchases, Apple Developer account, posting to discussions.apple.com, etc etc etc. The first time you use an Apple ID for a particular service, it generally goes through a little setup process to enable that Apple ID for that particular service. For example, the first time you use a particular Apple ID with the Mac App Store, it'll ask you to agree to the MAS terms & conditions, and enter/verify your name, address, and payment info. If you create the Apple ID in a service, the ID creation and service setup processes get done together.
iCloud is one of the services that can be set up on an Apple ID. Basic Apple IDs are free, but iCloud accounts cost Apple money (ok, not very much) because they include storage, email service, etc. Thus, Apple sets a limit on the creation of iCloud accounts. I don't think the limit is documented anywhere (and may change without notice), but last time I tested there you can only create three iCloud accounts (/set up three Apple IDs for iCloud) per Apple device (Mac, iPhone, iPad).
Your Mac has reached its limit.
Note that this three account limit only applies to the initial setup of iCloud services -- either creating a new ID for iCloud or using an existing Apple ID for iCloud for the first time. You can use as many iCloud accounts as you want on the Mac, as long as they were created/set up on other devices. Re-using existing iCloud accounts does not count against the limit.