Organ rejection from organ transplants is least common when donors and receivers are genetically related; As I understand it, this is because the antigens on the surface of the cells of the donated organ need to be unrecognizable as "foreign" ("allorecognition" in the case that the T cells mark the donor cells as foreign), requiring a genetic match in the major histocompatibility complex (MHC) on chromosome 6 (in humans). But from what I read, I couldn't determine whether 1) there were other histocompatibility genes outside the MHC, or 2) whether there needed to be an exact match between histocompatibility genes, or whether there was some proportion or threshold that would prevent rejection if met (or whether immune response against the organ is just proportional to the level of histocompatibility).
All of this is said the frame this question: Can localized (to a specific tissue or organ) gene therapy result in allorecognition? I imagine if those edits take place in the MHC, it could clearly cause allorecognition due to antigen difference, but are more histocompatibility genes sprinkled throughout the human genome? And even if there weren't, are there other genetic factors beyond antigen formation that can result in a genetically modified cell being rejected by pre-edit host T cells (aside from those modifications which stop the cell from functioning)