I never seen 'wage' following 'with' in dictionary; but it is very common for 'wage' following 'against' or 'on' instead as per dictionary suggests. This is while, I have seen many times in some notes or in movies that 'wage' is following 'with' i.e.
"Should the United States wage war with North Korea?"
"Making childern disappear is the war we wage with God. Makes people lose their faith. Turns them into demons like you." - Prisoners (2013) movie.
My question is that if 'wage with' in the above examples is misleading. I mean, although the writer is trying to convery that US may wage a war against North Korea, the sentence much means to me: US and North Korea ally and wage a war against another country! - which is not true.
What is your opinion?