How do you deal with the "everything is mine" stage with toddlers? He's been saying everything is…

How do you deal with the "everything is mine" stage with toddlers? He's been saying everything is his for over a month now. He'll try to take whatever it is too. He routinely tries this with my coffee which is definitely not his and he knows it. I'm getting real tired of it since now he's taking violets things like her clothes out of the drawers, he moves her bouncer around, and will take her pacifier out of her mouth which makes her upset. Then when I take it away he yells that it's his. He does it outside the home too like at the store he will grab something and when you try to put it back he screams that it's his and throws a fit. Ive tried explaining that not everything is his, and redirecting him with things that ARE his, but it doesn't work. He always screams it too, and if he doesn't throw himself at the ground it's a rare occasion.