Pardon my perhaps limited understanding, but "trans" quite literally means "opposite", so transgender == "opposite gender". "cis" means "same", so "same gender".
Both terms seem to imply that at the very least you fit in the two-gender construct, whereas nonbinary rejects that construct entirely. So I'm fairly certain that a "nonbinary transgender" can't really exist?
Then again everything is not so black and white and labels rarely fully fit, so perhaps it's a case of two partially fitting labels then?
Fair enough. It's just that what you seemed to describe as a nonbinary transgender just sounds like nonbinary to me. No reason why they can't want to change their genitalia, no?