For how higher incomes could end up middle class I wasn't thinking of a different threshold, but ways of defining social class that are more qualitative than quantitative.
For example you could define middle class as people who live a modest lifestyle financed by selling their labor to a company, and upper class as people who can live off wealth. So someone from a wealthy family living off a trust fund and going to an elite graduate school might count as upper class despite being low or middle income, and an engineer making $120k in the bay area might still count as middle class that way.
Defining it like that would probably produce a small upper class relative to the size of the middle class, but in historical societies where social class was a bigger issue what's considered upper class is usually a pretty small percent of the population, so it wouldn't seem too crazy to me to define it like that.
It’s a convention so, yes, it’s arbitrary (and people tend to change that definition to fit their points, and of course it’s relative to COL) but the most widely used definition is the middle quintiles. I believe this puts the upper bound around $120k for a household (not individual) in the US.
And you’re right, most people do consider themselves middle class. Some studies show as much as 90% of people think they are middle class which, unless we use a very loose statistical definition, is obviously false. The problem is people subjectively compare their life to their own peer group rather than society as a whole, so they are misled about defining the societal norm.