Scent related agitation is something multi-cat households have to deal with all the time and we've touched upon this in the past. Often the dynamics of the cat society can be difficult to maintain when there are new members of the family coming in. Something I have found particularly useful over the years in reducing the scent related stress of cat's is using an environmental spray which carries the synthetic chemicals mimicking those found in cat's lips.
The spray is of course Feliway. We have talked about the plugin type before to help keep cats calm or even happy, but the spray is another useful product for helping deal with cat's scenting and marking behaviours. As we've established before, cat's like to revisit their "spots" to check if they have been marked and if so, whether the scent is potent. We don't want the cat's to continuously mark areas with urine as it causes a lot of hygienic issues. In this case, the Feliway is sprayed and the cat will visit to find the area has already been marked, then move on.
The good thing about the spray is that it also has some feel good calming qualities so putting this inside pet carriers and cages help with calming the cat down drastically.
Remember, using the Feliway spray is not a solution to the underlying problem. Reducing the cat's exposure to stimuli for spraying is what you need to tackle.
Competing cat's in the household may need to be kept separate for a while until they can get used to each other's scents. Slow reintroduction is the only way to help transition the cat's out of competing cat anxiety.
In the worst case, with some households with alot of cat's the situation may only improve if the number is reduced.