It's possible to turn a verb into an adjective meaning 'want to...' したい, 食べたい or 飲みたい, but is there any situation where it makes sense to conjugate it as an adverb for words other than ～たくない?
食べたくなる — He suddenly wanted to eat, he became hungry, etc
死にたく行く — He went there with a desire to die, he went there wanting to die, etc
出たくする — He did so wanting to leave, he did it to leave, etc
or are all these grammatically incorrect or make no sense? I'm aware there are alternative ways of saying all of these phrases but I assume in these situations the nuance would be very different, emphasizing some sort of intent or motive