Using Gentoo might work if you enable the KDE overlay: https://wiki.gentoo.org/wiki/KDE/Ebuild_repository
Gentoo supports slots; which allows for concurrent installations of things like desktop environments. Not sure if it’s configured that way right now though.
If you use BTRFS you could install gentoo on a subvolume and boot into it when needed too.
I like the idea and have been meaning to build / find something like this however this does a little too much and in not quite the way I want. But it’s cool for those who need this exact implementation.