In the following sentence:
They can disagree.
what I want to say is that the subject, they, can possibly reach a state when they no longer agree. Of course, it can be the opposite - they can agree with each other and live happily ever after, but I'd like to specifically underline the chance for the negative outcome. So what I did is I took an antonym for verb "agree", disagree, and this was all I needed to build this very simple sentence. So far so good.
But what if I have a verb that doesn't have a simple antonym (or I just forgot this antonym and I need to come up quickly with a grammatical construct to compensate this)? Such as negotiate. Obviously, I can't say "they can not negotiate", because in English, "X can not Y" doesn't mean "X can possibly reach a state when X doesn't Y". It means "X won't do Y, never ever". But what should I do, then?
I can probably put a filler word between "can" and "not" to break this pattern, such as:
They can possibly not negotiate. / They can possibly not agree.
But is it correct, is it idiomatic English?