The liver is made of connective tissue and while the shape of the left and right is a little different, it largely does the same thing. Skin is also an organ made of connective tissue and can also be partially transplanted.
Other organs have a shape that is essential to their function. The heart pumps blood from atrium to ventricle in a series, if you tried to take half of it, it wouldn’t work. It has specialized parts that work together and can’t function without them.
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