Apple has never offered an upgrade license to go from the 10-user to unlimited-user version of ARD. It's always been a complete new purchase. The most cost-effective route now is to buy ARD from the Mac App Store. That version supports unlimited clients and allows you to install the administrator application on every computer you own or control (assuming this is not being purchased for a business).
You'll need to uninstall your 10-client version before purchasing anew or the old license may carry over. . Follow these instructions for the uninstall: