Warning! This is not a replacement for medical advice and I could be wrong. This is not my speciality!
If I'm understanding correctly seems like Mr. Mills had a marrow transplant, and the white cells in the marrow from the donor had attacked his liver. Chemoterapy is a poison, and liver's work is to deal and be distroyed by poisons, so this does not help.
Without donor's white cells, the Leukemia gets worse, but without liver, people die fast. It seems that restoring liver function would be the higher priority now.
Liver has evolved to be destroyed and regenerated. Is able to create new hepatocites massively if needed. Is said that you can remove 2/3 of the liver and the remain cells will regenerate a complete liver in only 2 weeks. Is an awesome organ if we think about it.
The options are, I suppose, a liver transplant/liver graft, that is expensive procedure but very effective.
or a liver support device that could buy a precious time until a liver donor is available
It seems that in USA there are around 4000 liver available from donors each year, and a list of around 17000 receptors. Liver transplant is expensive. You need to invest maybe $12000-250000 only for the operating teather part. Plus post-operatory procedures.
An alternative could be to take a chunk of liver of Mr. Mills and cultivate it in a laboratory, far from chemoterapy and vicious white cells and then create a bio-system that could act as an artificial liver for some time. A possibility maybe could be to make a self-transplant in the future. Even small chunks can regenerate a much bigger chunk of liver
Several types of artificial livers could help also to alleviate the liver work, like a Molecular Adsorbents Recirculation System (MARS) or/and fractionated plasma separation and adsorption (FPSA, Prometheus)