As a work colleague asked me about how I setup my "multi-live-system-thumbdrive": As a base I installed https://grml.org/ but I am sure another system using grub2 would also work. This installed grub on my USB thumbdrive with a rather simple main grub.cfg:
## grub2 configuration
source /boot/grub/header.cfg
insmod regexp
for config in /boot/grub/*_default.cfg ; do source "$config" ; done
for config in /boot/grub/*_options.cfg ; do source "$config" ; done