You are only allowed to have two working Creative Cloud installations. If you happen to have separate subscriptions for individual products then each single subscription is good for two machines. The same goes for a Cloud subscription, which is a single subscription - you cannot split up portions of that subscription across more than two machines.
Unless things have changed, if you install a subscription on a third machine it will automatically disable other installations. I don't think it only eliminates one.
See the following for details about the Cloud:
Creative Cloud Learn & Support
http://helpx.adobe.com/creative-cloud.html
Creative Cloud Help / Install, update, or uninstall apps
http://helpx.adobe.com/creative-cloud/help/install-apps.html