My story

In book one, I would create Agamemnon a good king. Instead of him being so selfish, I will make him a nice, forgiving and responsible man. Instead of refusing to give his price, he will give his price up because he would know it would be for the good of his image. Achilles would be loyal to him and he will give Achilles a fair share from the wars the he had won. The story might get interesting and the ending might not be a tragedy if Agamemnon was good from the start.
The ending might be peaceful.