Why my iMac is not allowing me to sign in with a new Apple ID?
Solution 1:
That Mac is likely now locked out due to automated processing to detect fraudulent account creation.
You'll want to use it with one of the 10 AppleID you made initially on it. I presume that after several weeks or months you might be able to make another AppleID - but you likely got flagged as abusing the AppleID system and would need to contact Apple and have your IP address white listed so you can create a large number of new Apple ID.
They do this for schools and businesses that need to make a lot of Apple ID - reach out to your Apple Sales contact or get together a list of the serial number of the Mac you have so they can see why you need so many new Apple ID at your site.
Otherwise, I would stick to making one test account and one production account and working with Apple to clear / reuse your test account for testing purposes. There are formal testing programs for education, business and if you are a non-profit - you might easily fall under either program to set up some test accounts for testing that don’t belong one-to-one to actual people using different devices.
Solution 2:
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.