Pippa under a table for protection! (please see base of post)
Introducing a new cat into a house with existing cats can obviously bring problems. We shouldn't forget that similar problems can result when people are thrown together. Think Big Brother, for example. I have some peronal experience of this (dealing with new cats not people!) even though I never actually asked for it. A couple of unrelated stray cats come in to get fed and stay for a long time sometimes. This has caused some complications with my existing darling girl cat who is usually very tolerant. (Note: one, the boy, is a full-time stray and the other is a time-share cat)
One of the strays is a boy who initially hissed and struck out at my girl cat and the other is a small female cat who is terrorized by my cat. A pecking order was immediately set up. The boy (Timmy) at the top, my cat next (Binnie) and little female cat (Pippa) at the bottom. OK so what happened next? Timmy still comes and goes and can walk close by Binnie without much of a bother. He might give a little hiss, no more. And Binnie will get quite close to Timmy indicating that things are settling down. After the initial problems of dealing with uncertainties, fear and defensiveness a method (an acceptance) of living together has set in.
As for little Pippa, a totally black cat with a Pixie face, she is keen to be here but Binnie has a go at her, perhaps because Timmy used to have a go at her (pecking order scenario, I guess). So, Pippa found sanctuary on top of the microwave, a nice high place that Binnie can't get to because Binnie is old and overweight and can't jump that high. This current set up allows Pippa to settle in and feel safe while the parties adjust and become familiar with each other. If Pippa keeps coming to visit, this scenario will probably keep going for about 6 months until things loosen up a little and both Binnie and Pippa are more relaxed together.
In my view, then, introducing a new cat is largely commonsense. It takes time (sometimes but not always) and it shouldn't be pushed along. Space is needed for all cats to find a refuge particularly new cats. In addition separate eating bowls might be needed and eating apart initially is probably a necessity. Both Pippa and Timmy don't use litter as they are stray cats so there are no litter issues but if they did separate litter trays would be required. The bottom line to introducing a new cat is that ultimately it will nearly always sort itself out with some initial supervision by us and time, patience and a sympathetic understanding from us.
However, the degree of supervision and acceptance amongst the old and new cat can vary widely. Clealy we don't want a small new kitten to be hurt psychologically through being terrorized by our existing cat (or hurt physically). That may ruin any future relationship. Careful supervision and a refuge are the initial answers I think. If there are too many cats in the household it may be impossible to bring harmony. The cats will be stressed. People should be aware of this and most are. Perhaps a maximum of 3 cats in a reasonably sized home is a good guide (what do you think?).
I think we need to be aware of the different personalities of cats. Some will be alpha types and some more timid. Some will be relaxed and some nervous. We should try and accommodate these traits in introducing a new cat. I think it also sensible to (ideally) carry out introductions at a time when things are calm in the home and when supervision can be conducted with care. I mentioned Pippa's refuge, the top of the microwave. That wouldn't be effective if Binnie could jump or if Timmy was having a go at her (which he isn't as I think he knows Pippa from his travels in the district). Normally, space allowing, a separate room that can be secured might be a useful refuge for the new arrival. The refuge room should of course be cat or kitten safe (e.g. no gaps and places where the new cat can become trapped and no escape routes). Obviously once placed in the refuge regular supervisory visits should be made and plenty of essentials such as bedding, food and water provided.
There is also the matter of our relationship with the new arrival. It isn't just about introducing a new cat to our existing cat(s). Our new cat has to get used to us and we are giants in the eyes of a cat. That for me, in any case, means plenty of TLC (tender loving care), a quiet voice, stroking (stroking the new cat and existing cat mixes scent as well), a very gentle, calm and slow approach - nothing to frighten but everything geared up to ensure that our new cat feels relaxed and settled. The reason why I am feeding two stray cats is because the homes they left were not completely comfortable for them. Cats like humans migrate to the best comfort zone. Although sometimes they might just simply prefer to time-share. I know Pippa lives with the neighbor but the neighbor allows her to roam across a busy road and it seems to me is not that involved in caring for her. I don't actually want Pippa to be here but as she is and as I can't stop her it needs to be dealt with in a careful and humane way. Introducing a new cat can be tricky and a bit worrying sometimes. My existing cat, Binnie, was also a stray (16 years ago). I went through the introducing a new cat process with her too - all was fine in about 4 months.
Note: Pippa's owner/keeper might read this. That is fine. I would ask her please to ensure that all is well at home and to see how she can keep Pippa from time-sharing. I'd rather Pippa stayed at her home.
Anxiety Drops, 15 mls might come in handy!