Just to clarify your question, if the organ cannot be transplanted there is no "recipient", since nobody receives the organ.
The brain is not transplantable in humans. It has been performed in labs on animals, with mixed outcomes. However in humans it is unclear whether there are any medical conditions which would actually benefit from a 'brain transplant', let alone other ethical questions of performing such a procedure.
The large intestine is not commonly transplanted because it is not necessary to sustain life (however it is medically possible). Likewise, the stomach, gall-bladder and appendix are not necessary for survival.
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the brain and the immune system cannot be transplanted
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Most organs (except the brain) can be transplanted. However only a few organs are essential for life (heart, liver, kidneys, pancreas, lungs, small intestine), which is why many organs are not transplanted - e.g stomach, spleen, gall bladder, uterus, overies, large intestine etc... are not essential for life, so are not commonly transplanted.
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The main organ which cannot get transplanted through one specie or human doner is the BRAIN.
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Anything can be transplanted. It is whether you mean "successfully" transplanted or not. Some things cannot be successfully transplanted (yet), such as brains. And some things are not transplanted (much) because they're not essential for life - such as limbs, stomachs (yes, not essential!), and large intestines. Limb transplants tend to be unsuccessful, as are other transplants where the thing transplanted is external - i.e you can see it. Ovaries have now been transplanted successfully (i.e have produced kids), but the procedure is not commonplace.