Final answer:
Matching MHC genes reduces the risk of rejection in organ transplants, but no graft is completely rejection-free. Localized gene therapy can result in allorecognition, especially if edits are made in the MHC genes. There may not be histocompatibility genes beyond the MHC, but other genetic factors can contribute to rejection.
Step-by-step explanation:
Although matching all of the MHC genes can lower the risk for rejection, there are additional gene products that also play a role in stimulating responses against grafted tissue. No non-self grafted tissue is likely to completely avoid rejection. The more similar the MHC gene match, the more likely the graft is to be tolerated for a longer time. Most transplant recipients, even those with well-matched tissues, require treatment with immunosuppressant drugs for the rest of their lives.
Localized gene therapy for a specific tissue or organ can result in allorecognition. If the edits take place in the MHC genes, it can cause allorecognition due to antigen differences. Although there may not be other histocompatibility genes sprinkled throughout the human genome, there can be other genetic factors beyond antigen formation that can result in a genetically modified cell being rejected by pre-edit host T cells.