How to modify the read-only system volume of the bootable external drive?

Hi, I have a bootable external disk and the system volume is read-only.

I’m using macOS Monterey 12.6.1. And both macOS Big Sur and Ventura have the same read-only system volume.

I know how to modify the read-only system volume in the internal disk.

  1. Boot into recovery mode to disable System Integrity Protection and Signed system volume.
  2. Reboot back into macOS. And create a new folder and mount the system volume there.
  3. Modify the files.
  4. Create a new snapshot.
  5. Reboot.

Here are several links taking about this.
https://www.reddit.com/r/mac/comments/wtjdsx/comment/il4ph2s/?context=3
https://dortania.github.io/OpenCore-Install-Guide/troubleshooting/extended/post-issues.html#writing-to-the-macos-system-partition

It seems that I can boot from the external drive and do the same thing to modify the system volume there.

But can I modify this read-only system volume of the external drive when I’m using macOS from the internal disk?

I tried the mount command above but it doesn’t work.

~ sudo mount -o nobrowse -t apfs /dev/disk2s2 ~/livemount
mount: ~/livemount failed with 75