Induced chimeric organs for xenotransplantation

A large part of the problem with creating organs using stem cells is getting them to turn into the tissues you want, such as muscle, rather than those you don't, such as bone. One line of research (I cannot find a link) into overcoming this has been to strip away the animal cells, leaving only the extracellular matrix , which would then be recolonised by human stem cells. The problem with this, of course, is that you stand a good chance of damaging the organ beyond repair, or else leaving animal cells which would trigger rejection of the organ or else risk diseases jumping the species barrier.

However, as homeopaths remind us, it is possible to repeatedly dilute a substance so much that the original substance no longer remains. So rather than try to get it right the first time, why not destroy most of the animal cells, repair it with human cells... and repeat the process until there is a sufficiently low chance that the animal cells will cause a problem?