더 키가 크고 싶어 vs. 더 키가 커지고 싶어 고 싶다 is used after a verb. 크다 is a verb and also an adjective In 크고 싶어, 크다 is a verb(to grow) In 커지고 싶어, 크다 is an adjective(big) an adjective + (어/아/여)지다 => a verb 크다+(어/아/여)지다 => 커지다 (to become big) cf. 작다 is an adjective(small) 작다+(어/아/여) => 작아지다(to become small) 더 키가 작고 싶어(X) 더 키가 작아지고 싶어(O)

~가 가지고 싶어. noun~가 가지고 싶어. Yea. its easy to get it. but you say "키가 가지고 싶어." when you really want to mean "i want to grow my height more." its very awkward. it sounds like this "I would like to have got height."?? do you want have a key? what mean?