Some directories can be moved, but you risk messing up your boot process if /lib, /etc, /bin, /sbin, and /dev are not on your root partition. Having /usr on a separate partition is sort-of possible, but even on Gentoo that’s an uncommon configuration, and I’d expect less flexible distros not to allow it at all. /var, /opt, /root, and /home can be wherever, though.

It may be possible to put only selected files in your /lib and so on, and then mount another partition on a different drive on top of the minimal one late in the boot process, or even to stopgap things with a carefully-designed initramfs, but I think you’d be looking at some trial and error (and make it more difficult to update basic system packages).

Also, defining what is “just the OS” on Linux is not as easy as you may think. The smallest possible configuration that will get you a running system is a Linux kernel + busybox (a set of cut-down system tools that includes a simple init system, a shell, and a basic device manager). Most of what your distro packages is not part of the OS, strictly speaking—it’s optional add-ons that the people making the distro think most users will find useful.

@Ozzy Exactly what I was thinking. Kind of a PiTA if everyone needed to do that, but maybe an excuse to throw up an open-source script on github for it.

Take a look at this, might be interesting: https://wiki.archlinux.org/title/Overlay_filesystem