No, you should install any versions of BBC Symphony Orchestra to the same library folder called 'Spitfire Audio - BBC Symphony Orchestra' in one location only.
This will ensure that the plugin will look for the content of all three versions in that location, enabling the Mode Switching function.
You can have any of your versions of BBC Symphony Orchestra installed on a second computer, but if you want to install multiple versions the same will apply: all should be installed to the same library folder.