This is the Austro-Hungarian Empire
Austria-Hungary was an amalgamation of the Duchy of Austria and the Kingdom of Hungary under the Habsburg Dynasty, which ruled as Holy Roman Emperor also from the 1500s.
The Emperor's line came from German stock, which made up 23% of the population (in the 1910 census). In 1848, due to the low population of Germans, the Emperor had to give the Hungarian minority (about 20%) its own Parliment. The Emperor also held a third major dynastic title as kind of Bohemia (Czechs where 13% of the population).
So the 'ruling' people were barely 1/5 of the total population. There was a lot of nationalist resentment at the Germans pushing their language on everyone else. When the Hungarians got their own parliment, the nation became functionally tri-lingual: all administration had to be carried out in German and Hungarian and whatever the local language was (Czech, Croatian, Polish, Ruthenian, etc).
Ultimately, this didn't work out well at all. You mention the 1910s; well Austria-Hungary didn't make it out of the 1910s, dissolving at the end of WWI.
Its Russia too!
For another comparison, the Russian empire of Tsars was peopled by about 44% Russians in the 1897 Census. It too failed due to the stress of WWI, collapsing in revolution in 1917. The various parts went their own way for a while, but eventually everything except Poland was reunited with the Soviet Union by the early 1920s. The Soviet Union, you may have heard, didn't prove to be long term stable either.
And the Ottomans, maybe?
The Ottoman Empire was certainly polyglot in the late 1800s, but by th early 1900s it had lost much of its non-Turkish parts. The official census from 1914 makes it 80% Muslim, but doesn't distinguish between Turks and people who would not consider themselves Turks, such as Albanians, Kurds, and Arabs. In any case, the Turkish population was definitely low in the early 1800s when there were several million people in the Balkans and millions more in Egypt that were part of the Empire.
The time around 1900 was a bad time for polyglot empires. They generally fell apart on their own, and whatever stability they had was wrecked by World War I. None of the highly multi-cultural/multi-lingual empires of Europe survived.
I think it is safe to say that your Empire is doomed, especially if they get pulled into a great power war.