Tony tries to threaten/shut Jameson down for all the defamatory things he posts, but Spider-Man’s identity is secret. So is a good portion of his activities. So Tony can’t shut it down w/o revealing Peter’s identity.
Jameson is the kind of person who just gets angrier when threatened, and will go after Spidey twice as hard when he realises the vigilante has Iron Man and the Avengers’ support. But Tony is also not the kind of person to back down. Jameson pisses him off and he’s seen the way Peter’s shoulders slump when he sees those awful, awful headlines, the way people automatically hate and distrust the teenager bc of the unfounded poison Jameson publishes, and Tony is going to do something about it if it kills him. Buying out the Bugle’s buildings is definitely something he would do. It is war between the two men. Peter has flat out made Tony promise not to buy out the Daily Bugle and pull it under - “People’s incomes depend on that newspaper; I can’t stand for hundreds of jobs to be lost just because they’re mean to me.” - but Tony is sneaky. He’ll intercept Jameson’s coffee orders to make them stale decaf. Slyly give Bugle reporters bad info about Stark industries and then publicly come out with different information, showing off their untrustworthiness. And, ofc, buying out the entire building, multiple times, just to piss Jameson off.