We create a system where corporations can give politicians an unlimited amount of money (Citizens United Supreme Court ruling) by saying they (corporations) are people and have a First Amendment right to free speech, thus allowing them to spend to their heart's content.
Then we prosecute a politician who takes the money the court rules is legal to give.
If we are going to go after pols who are influenced by donations-donations they need to win reelection-then lets ban all donations to political candidates and go with public financing and require the media to provide free air or print time to all candidates from recognized parties.
Get the money out of politics. Of course, that may mean no-one will want to run.