Hello Dr Rob.
You may upgrade your Parallels Desktop 9 to 10th version buy purchasing _two_ upgrade keys.
If you need one more Parallels Desktop 10 license, please purchase a full Parallels Desktop 10 key.
Because Parallels Desktop 10 upgrade key won't work alone, you have to provide an additional Parallels Desktop 9 full/upgrade key to use it.
In Sum: 2 upgrade keys, 1 full in your case.