The approach we took was to keep the new cat in a separate room for the first few days to allow them to begin to get used to the new scent. We would then swap blankets to give them further time to get used to each other's scents. Then we'd open the door and allow them to interact under supervision for short periods and then we gradually increased the time they could interact each day.

I'm not sure this would work if you had outdoor cats. We didn't actually intend to get the third cat, but we ended up taking him in as our friend's original cat refused to acclimate to the point that he was spending all but 20 mins a day outside of the house and so they needed a good home for their new cat.

Cat colonies, as I understand, tend to follow the the eighth rule of Fight Club, which can make introductions seem unsuccessful even when they may not be.