My experience is that they'll always find a way to live together with tearing each other to shreds but that they don't always come to enjoy the existence of the other.
Our worst cases were always introducing kittens to older cats but I've heard other people say that is the best way to go. Once, our existing cat never acted aggressively or put out by the new cat. She just started peeing all over the house (and, worst of all, frequently into the stove burners). Because of the timing we though it was the new cat until she was caught in the act.
It stopped immediately when we passed the cat on to another family. (This vengeful pee-er was the same cat that figured out all on her own and very late in life, with absolutely no prompting form us, to pee in the toilet.)
Unfortunately there really isn't any way to know how it will go since it so depends on the personalities involved and frequently a few days of tenseness before they decide to like each other (if they do).
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