I wanted to know, are there stories in which the protagonist becomes much more of an antagonist, doing something to the main villain that makes the reader kind of "sympathize" with the antagonist, even if only temporarily?
Try Lolita, American Psycho, Enduring Love, The Talented Mr Ripley. They all have protagonists who act at some/many points like antagonists. Although its not really as a result of doing anything to a 'villain'...most of them are a little more complex than having a clear-cut hero/villain conflict. And they're all lit fiction, not sure if that's what yu're writing (not that it should matter because good writing is good writing, and those are some of the greatest novels ever written (especially the firs two).
Memento would be an excellent example of this, where the main protagonist is also the antagonist of the piece, even if found out in retrospect. Could also look at Pride and Prejudice and the treatment of Mr Darcy by Elizabeth throughout the book, and how he changes from antagonist to protagonist in her eyes, also a lit fiction book.
Not sure how relevant this is... but it happens alot in the Law and Order series. If you are not familiar with the show its a cop/court procedural. Where for the first half or so of the episode a couple of detectives try and solve the crime, and the last half involves the courts and such. Well depending with series I suppose. Criminal Intent has a very different formula... Anyways. Often times there will be a murder or attempted murder. Sometimes the detectives will uncover something in the killers past or what the victim themselves helped do to others. So it isn't uncommon for your sympathy leans more towards the defendant rather then the victim. Doesn't always happens, and often times they are just cold hearted killers. Does this make sense? But yeah there are stories like this.
Yes. Read Death Note and you'll see all the sympathy switching you could handle in 110 manga chapters.
maybe it's just me, but i've always felt bad for the antagonist when i was growing up. The best example is Gaston from Beauty and the Beast. He's a selfish idiot obsessed with beauty, but in spite of the nature of his actions, the fact that he would go through so much trouble for the woman he loves is admirable. A beast had stolen his love's heart and what does he do? He goes off to slay it. He's brave, he's strong, and he's determined to get the girl. In a different context, he would be the hero. I'm actually writing a story where everyone believes my MC is a villain because of a prophecy, but he's actually a good person. I like villains. they're almost always more interesting than the hero. edit: apologies if this was off topic. just felt like adding my 2c.
Gaston isn't doing it out of love, he's doing it because he thinks Belle is hot, and then his pride is hurt when she rejects him, which he won't stand for, hence his persistence in chasing her. It's not out of love, its out of a desire for revenge. The fact that he goes to such great lengths for his own pride and satisfaction makes him the villain.