Fix the litterbox situation.
It's often the case that if a cat is bullying, it's over some particular thing, just like how two kids might get along perfectly until you add in some really cool toy to the mix, and all of sudden they're fighting over it.
In your case, almost certainly your cats are fighting over the litterbox. Perhaps the bully sees it as a great way to trap the victim, or perhaps the bully doesn't want to share. The result is the victim is now afraid to use the litterbox, and going all over the house.
You should attempt to address both possible reasons, by making the existing litterboxes less of a place to be trapped, and also adding additional boxes. I would remove the lids from any existing boxes and move them when possible to be more central in the room. That way, your cats can escape the box from any direction.
Find and fix any other points of contention.
There may be other places where bullying incidents tend to happen around your house. You should keep note of the exact spots where the incidents happen. If you notice any spots where there's a pattern of bullying, now you need to stop and think what may be the cause, and what you can do to make it no longer be a cause. For instance:
- They're fighting over something they all want to use. Water bowls, beds, litterboxes, and so forth. In this case, it helps to just buy more of the thing they're fighting over.
- The bully is ambushing the victim in particular spots. For example, the bully likes to hide under furniture, or around corners, and then when a hapless victim walks by, they strike. In this case, try to either block access to the area, or provide an alternative route, so the victim doesn't have to walk right by it to get to the other areas of the house.
- The bully traps the victim in some place they can't get out of without going past the bully. Cat caves, cat trees, cat shelves, and so forth, are all places where the victim cat could be potentially trapped. In these cases, you should use more cat furniture or rearrange your existing furniture so that the victim has more than one exit route, and so they can't be trapped anymore.
Make sure the bully is entertained.
Sometimes cats bully simply because they're bored, so make sure to play with the bully especially until he is tired out. Cats will play in a series of short bursts. In between bursts, they'll sort of sit and watch, but that doesn't mean they're actually done. You should keep playing until your cat truly seems uninterested.
It's also a good idea to provide your cats with things to keep them entertained even when you're not around. Keep a variety of toys out. You might even rotate toys. Also make sure they have access to windows, which is a great form of cat entertainment. Or you might even try food puzzle toys. Whatever keeps them from getting bored.
Try to encourage the victim to be more confident.
Bully cats like to target victims that look weak. Therefore, it helps a lot if you can get the victim cat to feel more confident. Seeing a more confident cat makes the bully less likely to bully, and it reinforces the victim to be confident.
- If there are areas the victim avoids due to the bully cat, try to spread the victim's scent in those places. You can do so by moving things like blankets or beds the victim sleeps on into those places. With the victim's smell more spread around, the victim cat will feel it owns the space more, and help make it more confident.
- Get both the victim and the bully cat together in the same room, but keep them both distracted from each other as much as possible through play, in regular sessions. You will need a second person to help you do this, one person per cat. A cat playing uses much more confident body language, and the bully will be able to observe that. Meanwhile, the victim will feel more confident because they were in the same room as the bully, and nothing bad happened.