It is possible to install other versions with update-pepperflashplugin-nonfree command.
If you list the contents of the script you will find options to install unverified, beta and unstable versions.
I think i tried unverified versions, but now I am back to stable I think. I am not sure because the status request is a bit, bah:
sudo update-pepperflashplugin-nonfree --status
Flash Player version installed on this system : 126.96.36.1996
Flash Player version available on upstream site: 188.8.131.52
But at least it is possible to try
sudo update-pepperflashplugin-nonfree --install --beta (or --unstable/unverified)