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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.
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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 ...
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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
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