This worked for me and might not work for your.
Try it at your own risk!
$ wget -qO - 'http://archive.neon.kde.org/public.key' | sudo apt-key add -
$ sudo apt-add-repository http://archive.neon.kde.org/user
$ sudo apt-get update
$ sudo apt-get install neon-desktopUpgrade everything. Repeat if necessary, until everything is really up to date and you have no held-back packages.
$ sudo apt-get update
$ sudo apt-get upgrade
$ sudo apt-get dist-upgrade
How I fixed (Ubuntu 16.04 Xenial) non-upgradeable state after doing the above (
sudo apt-get update --fix-missingdpkg –configure -aapt-get install -fdidn't seem to help but may):(after EACH step below, do
sudo apt update && sudo apt upgradeandsudo apt dist-upgradeagain)apt installpackagename(actually for MANY packages, so pasted them [list of packages held back may be found via apt upgrade or apt dist-upgrade] to a list file then installed mass packages from a file)
apt removepackagename (as shown in upgrade or dist-upgrade conflict error such as: "packagename breaks something but packagename-y is set to be installed").sudo apt install neon-desktopagain since some of the removed conflicting files were dependenciesNow my desktop works better than ever (faster and more stable) even though the system was changed from Ubuntu to Kubuntu (where I did a similar) to Neon!