campaign for (someone or something)
1. To strongly support someone or something and encourage others to do the same; to fight in favor of someone or something. Many people in our small town are campaigning for that big construction project because the closest store right now is 10 miles away.
2. To support a candidate pursuing an elected office and encourage others to do the same. I'm campaigning for Caroline in the race for student council president—here, have a button!
campaign for someone or something
to support actively someone or someone's candidacy for political office. I would be very happy to campaign for you. I want to campaign for the winning candidate.