brent
In my opinion you should not run them side by side or share $HOME with another distribution or different editions of the same distro.
While gnome and budgie are less likely to set each other on fire, by default gnome uses gdm and budgie lightdm. Note that the display managers are set as conflicts of each other 1, 2. Install one the other gets removed. I think both can use gdm but I am not really experienced with that and either way it would be different to a regular install.
Plasma has historically had issues coexisting which is why instructions for installing it side by side do not exist in the help center. The maintainer had enough of support requests for issues that only occur if you do this. So they are not found in testing and hard to troubleshoot.
Ultimately if you wish to switch DE's, reinstalling remains the recommended option. But ultimately it is your system, your decision.
