What definition is the OP interested in? I will guess at a definition and play with that, as I think that is what they want.
WI American Empire – It was a continental empire. Perhaps the OP would be satisfied even with a French-style globe-spanning empire run by a Republic.
This alternate America simply decides before the 20th century that it wants to be a “sun never sets” empire like Britain’s or France’s, with possessions on nearly every continent and every ocean.
While it would require *a lot* of change in American political history, but it is not impossible for the US to set a goal in the 19th century (probably late 19th) to become a globe-spanning empire equal to or second only to Britain. Avoidance of the US Civil War (or avoidance of one that lasts more than a year) might be a threshold condition that allows this to happen.
What thinketh the OP? The other discussants?