I'm trying to understand which problem (use case) you actually want to solve.
It looks like you do not actually intend to modify your system files, but to change something in your GUI.
If that's right, see below.
Usually, the best way to make personal changes to files that are part of Ubuntu, is to make a copy of it to your personal files, and modify that. If you can read the file owned by root, you can create a copy, which is owned by you.
Some GUI features even do this automatically in some cases.
As a simple example, if you want to make a change to an existing desktop wallpaper image,
you could find the file, copy it, and modify your copy.
Now you can use it as wallpaper image.
(Doing it this way has various advantages, like keeping the original, not creating conflicts when updating the package it belongs to, allowing to do the same for multiple users (and probably more).)