Technically Shepard is some sort of Cyborg after he got reassembled in ME2.
I mean he/she was just squish when they began restoring him/her. They proceeded to replace almost the whole skeleton with tech and possibly did the same with the organs too.
I don´t think that you can fully grow new organs, but as Aveline wrote. We don´t know all races in the Milky way and perhaps there are a few minor races that can do it.