Install your third OS on an empty partition or add it to a new disk.
From the disk with the grub installation, ensure os-prober is installed and rerun grub-mkconfig to find the new OS and add it to the grub menu.
Disabling the IOMMU might help.
Looking at the output from lspci, it's obvious that there's no PCI device there that would correspond to a SD/MMC host controller. This explains why the mmc driver modules are never loaded (loading the modules is triggered when a matching device appears).
I've never seen that particular machine, so I don't know for sure what ...
Ubuntu 19.10 is an EOL Ubuntu release. It is recommended to upgrade your distribution.
To continue using an EOL release, you need to adjust your /etc/apt/sources.list by replacing the URLs with http://old-releases.ubuntu.com/ubuntu/, then run:
sudo apt update && sudo apt upgrade