I'm so glad you found TCS, and I hope we can help. We moved into a new home and had problems with Spooky - and they weren't medical.
But I do know the stress you're talking about!
1) I realize the resident cat is not in a new home, but as Gaye pointed out, the stress of having three new "companions" she (right now) doesn't want could have caused a UTI. So it's best to at least eliminate that as the reason first. Peeing outside the box is not always due to medical problems, but when they have a UTI, they almost always pee outside the box. So it is best to rule that out (or in) first.
2) If it is not a medical problem, she is stressed, and that's why she's doing this. However, if even she begins to de-stress, the scent of where she peed before will encourage her to pee in those same places. The scent of where she peed outside of the box MUST be cleaned in such a way that she can no longer smell it - and their noses are far more sensitive than ours. If you haven't already, get an enzyme cleaner. This is the ONLY thing that will work. They sell stuff like Nature's Miracle in most pet stores and supermarkets. It works, but we found that we had to treat areas several times. This product always worked the first time around for us: http://www.nokout.com
. Blot up the pee. Then you completely soak where she peed - and I mean completely. If on carpet, it's got to get down to the floor boards. Let it sit for 10 - 15 minutes, then soak up excess wetness. Then just let it dry - and depending upon the area, it may take up to a few days. We always put aluminum foil over it (just placed it over it) while it dries. If it's on something washable, you can add the nok-out (I don't know about Nature's Miracle) to your wash like you would a fabric softener, and that works.
3) Try the feliway diffusers. It can be expensive, but they often help. You can also consider also using Flower Essences - a Rescue Remedy or Multi-cat Harmony remedy may help as well: http://www.catfaeries.com
4) A lot of cats that don't have a peeing-outside-the-box problem sometimes pee on bathroom rugs. There's something about the backing on them that often smells like ammonia, which to cats means is a place to pee. We got rid of the bathroom rug that had a backing and use just a cloth one, and that worked just fine.
5) Add extra litterboxes and keep them REALLY clean. The rule of thumb is that you should have one more litter box than cats, and you should have litter boxes available on each floor the home has. She may not want to pee in a box if one of the other kitties already used it. So keeping the really clean and having lots of boxes can help relieve the problem. If you already have four boxes out, consider adding another one or two. I know it's a lot of work - but the extra work can be worth the relief of not having a cat pee outside the box.
6) Your boyfriend (and you) should be giving her lots of extra love, attention and reassurance (I'm sure you already are). Positive reinforcement can really help. Any time you see her use a box, praise her to high heaven and even give her treats. Try to avoid getting upset with her, as she doesn't understand that what she's doing is wrong, and yelling at her when she's peeing outside the box can make the situation worse. A sound, firm "No" won't hurt, but leave it at that.
7) You may have to confine her to a small room for litterbox retraining. She should have food, water, and a litter box. Make sure you spend time in there with her, reading, or whatever. It doesn't only have to include interacting with her while you're in there. When she's successfully peeing only in the box, let her out for a few hours at a time, and keep increasing the amount of time she's allowed out.
8) If she totally stresses at being confined to a room, talk to your vet.
The last resort: A lot of people do not like to medicate their cats. We not only moved to a new home, but we adopted a troubled teenage daughter. We did all of the above, and ended up having to confine Spooky to one room for litterbox retraining. She started obsessively licking. That day. By the next day, she had some large scabby bare patches. It was just too much. We talked to the vet, and decided to put Spooky on Elavil. It is an antidepressant - but it also causes the cat to retain urine, so she doesn't want to pee frequently. From day one on Elavil, we had no more peeing outside the box problems. She would take one really large pee every day, and it was always in a box (that we still kept really clean). We kept her on Elavil for about 3 months, then slowly weaned her off of it, and everything's been fine since.
Thank you for wanting to do the right thing for all the kitties and working through the problem