I - think to - have successfully installed Qubes OS 4.0.3 on an external USB disk.
I used a 16GB USB drive to write the ISO to, booted from it and then installed it to a different USB drive of 64GB.
I got some installation success message, but the system did not reboot, it was hanging with a black screen and some “The system is now rebooting” or so message.
The newly installed system in fact was not able to actually boot on starting from scratch.
I followed the “Boot device not recognized after installing” instructions at qubes-os.org/doc/uefi-troubleshooting/.
Now the system boots - but not completely: I can’t get an X system up. I see lots of boot messages and then at some point there is a “The SESSION_MANAGER variable is undefined” error and then a series of other error messages (can’t copy paste) indicating that it just can’t start the X Window system. After several retries it then stops trying and just hangs.
Can’t enter some other tty with Ctrl-Alt-Fx for example.