I have a male Angora cat.
The problem is that it keeps doing acts of sabotage, playing with litter, dropping vases, cracking cups, etc.
We also have 3 other cats in the house (his "wife" and their 2 "children"). He keeps hurting them.
I think your cat may be bored. Bored cats find things to do, including chasing other cats, knocking things onto the floor and destroying them.
A good way to discourage this is to get the cat a good big cat activity centre, which it can enjoy using to climb on, play with and scratch, and load it up with different kinds of toys, such as pingpong balls, catnip mice, etc, which can be knocked onto the floor harmlessly. And spend a good while every day playing with him using a cat wand or feather toy or similar, so he gets a chance to use all that energy up.
Also, try cat-proofing the house. If possible, put fragile easily knocked off items into a no-cats space or a cupboard with a door!
You may also want to ration his access to the other cats. It's no fun for them if they are with a cat who is a bully, and if he's constantly practicing chasing and upsetting them, in my experience he's likely to get worse. I have a bully cat, and he is only allowed around the other cats when I'm there to make sure his behaviour is appropriate. His behaviour has improved a lot since we started doing this. Time-outs can work well for cats.
It's important to understand that cats have a very different psychology than dogs or humans do. Like us, dogs are pack animals. Co-operation and pleasing the pack leader are survival skills that work in our favour when we want to train them.
Cats, however, are mostly solitary hunters. They don't have the same instinct to please that dogs have. This does not mean that cats don't love their humans, but it does mean that they perceive relationships very differently than pack animals do.
Your cat is not dropping vases and cracking cups to be mean or even disobedient. Perhaps it's doing so because it's fun, or because those objects are in its way, or even just by accident. If you yell at the cat for doing these things, the cat won't understand that it has broken some rule. The most likely result is that the cat will become nervous, and perhaps break more things out of anxiety-induced clumsiness.
Preventing the cat from breaking vases and other ornaments that stay in one place is pretty easy. Get some blu-tack (or something similar); it's a substance that looks a bit like chewing gum, and can be used to stick things in place. Problem solved, and your ornaments are safe from earthquakes and clumsy humans as well!
Are there surfaces that you want the cat to stay off of? The best way to prevent a cat from doing something is to make it unappealing to the cat, but without frightening the cat. Many people keep a spray bottle of water handy, and when the cat jumps onto the forbidden shelf, it gets a squirt. This doesn't frighten the cat (who probably won't even associate the squirt with you) it just makes it associate something unpleasant with being on that shelf. There are lots of options here. Rather than a squirt bottle, I just clap when I want my cat to stop doing something. I only clap once, and not very loudly, just enough to startle but not frighten her.
As for fighting with the other cats, the squirt bottle can work well there also. Whenever a fight occurs, spray the combatants. But also make sure that there are lots of places where the cats can get away from each other when they want to be alone.
You'll find loads of other tips on this site for specific problems. Good luck!
Via keshlam in comments above: "Odds are that none of this is sabotage or malicious. Some of it is just being a cat. Some of it is things you need to explain to the cat that it can't do. And some of it sounds like you may be inadvertently encouraging, by giving the cat attention when it does them."
My cat is an absolute angle; she never knocks anything over. Unless I'm watching her. She'll even look back, miming at me: "Oh, no. Look this thing... it's almost falling over." {nudge}
When she does this, she's asking for attention. Don't make the mistake of training them that this is how you get play time. Provide a brief distraction, possibly a scruff if you really think it's necessary, so that they don't make this association.
But you still need to play with them, even if they break your favorite vase. Affection must immediately follow discipline (pet them for a bit after a successful scruff; that means they flopped over and submitted), but discipline must also consistently follow bad behavior. These situations should happen less often as you better establish your dominance (every time you scruff) and The Rules.
