Bottom up rather than top down - you need to help her build the skills and encourage the behaviours you want rather than trying to squash the behaviours you don't want.
So for the plate example, the missing skill is probably a combination of cognitive flexibility (being able to accept changes from what she expected) and emotional regulation (not ramping up and up and up when this happens). Of course both things are still in development at 3.
In the moment, you just deescalate, keep everyone safe, reiterate rules as you said e.g. I won't let you hit, and taking some slow deep calm breaths in front of them often helps because a lot of children will automatically copy which helps them calm down too.
Don't address the behaviour in the moment apart from to control the environment and keep everyone safe (physically stop hitting/block access to the other plates etc) you could name the feeling. Try to avoid the word "but" eg "I know you wanted the other plate, but this is the one you have." Just focus on calming down. You don't need to persuade her to accept the other plate as once she's calmer she probably will accept it, you just have to go through the strop first. If the argument was about something like asking nicely, you might have success after she is calmer getting her to ask in a slightly less rude way and that's a win, but getting through the outburst is a win anyway. Don't expect to be able to use it as a teaching moment.
Outside the moment, you can work on things like emotion regulation by talking about feelings (at every bloody opportunity
), when you're playing with Playmobil people or toy animals act out their feelings dramatically, try looking for books about feelings, Daniel Tiger has some good episodes, watch Inside Out. Any time you have a feeling, narrate what you're doing to help with it, e.g. "I'm feeling a bit cross so I'm going to take a break from this and do something else". The How to Talk books are good too, you might have read them before, they are worth a re-read.
Cognitive flexibility can be practised with role play where you swap roles, like switching between being customer and cashier in shops/restaurants (also try adding things like I'm an angry customer, you're a scared cashier) games where the rules change like Simon Says. Don't let her win all the time or avoid games with losing, but make it very silly when someone loses and model losing in good grace. Make it very quick to get back into the game after losing. This is easier to do when there are more than just two of you, but you could start out where you're the loser if you want. IME it's incredibly helpful to get the message in there bit by bit that losing, making mistakes etc is not the end of the world.
Because you're doing all the teaching outside the moment it's a bit more proactive effort, so it can also help to try and keep a bit of a diary to keep track, see if there are patterns, there might be something you can trace to things like diet, sleep, time of day, toilet needs etc which helps with managing it.
Also you obviously can't work on everything at once, so it can help to make a list of your 5 or so top issues and then think about what underlying skills might need strengthening. If I have no idea I've asked chatgpt before as a starting point e.g. "In child development, what skill underlies the ability to..." And then what the normal developmental timescale is for that. Then I fact check it on more reputable websites, but for example I'd never have known the phrase cognitive flexibility - and knowing that lets me Google games and activities to try to strengthen that.
When you know which skills need more support you can also move the goal closer to her a bit. So for example if she struggles with unexpected things, you can let her come into the kitchen before dinner and choose her plate, or if you know what her favourite is, give her a heads up e.g. DD, I know you like green but the green plate is in the wash, we have yellow today. Or you might decide you're sick of plate arguments and swap all plates for the same colour.
Good luck! Other books I love are When Your Kids Push Your Buttons, for processing your own stuff, and Big Baffling Behaviours, which is good for spotting the moments where their "wise owl brain" has flown away and also identifying when it's back. (Obviously this is a metaphor!)