Okay, so vital to the Holy Roman Empire was the idea that they were the true successors to Rome, and they styled themselves as emperor to legitimize that. Other rulers mostly styled themselves as kings, and those who did style themselves as successors to Rome, such as the ottoman sultans, specifically refused to refer to the Holy Roman Emperor as being an emperor. However, at some point the idea that there can only be one emperor very clearly stopped, with multiple rulers styling themselves as emperors, and everyone being OK with that. What caused this change?
Here is a link to a list of empires and "empires" in the western European cultural sphere.
http://historum.com/european-history/121800-empires-western-european-cultural-sphere.html
Note that from 800 to 1204 and from 1383 to 1721, or 742 years, there was only one empire in the western European cultural sphere. And from 1204 to 1383 both empires in the western European cultural sphere claimed to be the Roman empire.
Of course it was known that in the eastern European cultural sphere there was another Roman Empire, but each one claimed to be the one and only genuine original Roman Empire.
There were also the imperial claims of the rulers of the First (913-1018) and Second (1185-1396/1422) Bulgarian Empires and the Serbian Empire (1346-1371) as well as the several competing eastern Roman empires after the 4th crusade in 1204.
Since almost all the Bulgarian and Serbian Tsars used the titles of "Emperor of the Bulgarians and Romans" or Emperor of the Serbs and Romans" their realms might be considered semi or quasi Roman empires.
For a few years around 1230 there were five competing Roman Empires in the eastern European cultural sphere and from 1355 to 1371 there were six.
But in the western European cultural area there was only one Emperor except for the Emperor of Romania (1204-1383) who claimed to rule in the eastern European cultural area.
It was not until 1721 that someone claimed to be a non Roman emperor.
In 1800 it was proposed that George III take the title of emperor when great Britain and Ireland merged into the United Kingdom, but he declined.
And then the floodgates opened and non Roman emperors multiplied.