The erasure of all monarchy and replacement of it with global liberty and republic?
Intriguing.
The thing that makes it not too impossible is the fact that, America was founded on the principle of the Enlightenment, and solely on that. It wasn't a territorial dream of nationalism based on an ancient foothold for a certain ethnic group. It was founded a new kind of country. Due to this, I could see some change in ideals which leads to "Manifest Destiny" expanding to a "Spreading the Republic across the world" and such things.
It'd require significant changes, though, in early US foreign policy. The first step might be in agitating for all of the Americas becoming independent, so that when the Spanish colonies break free, they seriously contemplate becoming part of the USA, and the country becomes the "United States of the Americas".
That kind of thing would be the first step towards a global Enlightened Republic led on American classical-liberal ideals.