The Number Dress-Up Party

I created the Number Dress-Up Party puzzle way back in 2017 and every so often I stumble across it again when searching Twitter for other stuff. When I stumbled across it today, I decided it was time to write it up in a blog post.

The puzzle goes like this:

The Number Dress-Up Party
All the numbers have come to a dress-up party in full costume. They all know themselves which costume everyone else is wearing, but you don’t know.
If you pick any two of them and ask them to combine with +, -, × or ÷, they will point out which costume is the correct answer, and they’ll happily do it as often as you want. For example, you might ask for robot + bear and they will point to unicorn. (If the answer isn't at the party, they'll tell you that too.)
How do you correctly identify the numbers 0, 1, 2 and 3? How do you do it in as few steps as possible?