I suggest you avoid using words that you do now know that meaning of if you want to be able to add anything meaningful to a discussion

Care to provide any evidence for your claim? At the very least put in the work to redefine the word empire to have such a broad and expansive definition that the US would qualify

Multiple definitions I guess. NATO countries are very much part of the US empire but pretty much all the countries that we have military bases in would be part of a looser definition of the US empire.

We can control international relations that most of Europe, Canada, Australia, Japan, and South Korea have to a fairly strong degree.

I would say this along with us having had fairly strong influence in the economies of these countries historically and our ability to easily coordinate military operations with them make these countries part of the US empire.

And yet NATO countries can leave NATO. Until subject states in an empire countries want to join NATO, not exit it.

But sure, that is the expansive redefinition of the word I was looking for.