Present day Roman Empire

[The Mikado]

Pretty much the only realistic scenario in which there's a state named "Roman Empire" around today would be if Catherine the Great followed through on her dream of conquering Greece away from the Turks and forming a new Byzantine Empire based in Constantinople, with one of her grandkids on the throne. This revived Eastern Rome would have parts of modern Greece and Bulgaria, with Constantinople as its capital (maybe reaching across the straits to snag the opposite sides of the straits), and a Romanov cadet branch on the throne. This would be squarely a Russian puppet state and its main purpose of existence would be to keep the Bosporus and Dardanelles open for Russian naval traffic and trade. It would probably fare little better than the Ottomans did regarding the rise of nationalism and would probably eventually lose lots of land to Bulgaria and the Turks, but could conceivably be an imperial monarchy well into the 21st century. This "Byzantine Empire" would de facto be Greece and just Greece (plus Turkish Thrace) by modern times, but could have its "Emperor" and a much more elevated Ecumenical Patriarch because he'd be in a Christian city.

[The Mikado]

Napoleon allows Prussia a standing army of 105,000, allowing Prussia’s leaders to be more adamantly pro-French. Napoleon never invades Swedish Pomerania, instead pledging Finland to Bernadotte. Recognizing his ability to turn and march against Russia, Bernadotte declares a full alliance with Prussia and France after several rounds of diplomacy, and the three armies march against Russia. With 85,000 Prussians and 35,000 Swedes joining his efforts, besides the Danes, Austrians, Italians, and Rhine soldiers, Napoléon makes it to Vilnius by September 1 and calls for a halt. However, Leberecht von Blücher takes 150,000 men, half of them Prussian, and marches on Kiev. He manages to make it there by October 28, and he calls for a halt. With the 600,000 men in Vilnius, Russia is forced to split its forces. Although used to Winter, they suffer heavy casualties in the December Offensive and heavier casualties still in the February Attack, leading to a rout. Saint Petersburg and Moscow are taken, the latter three weeks before expected. (Prussian and French cavalry made a secret march as the main army distracted the scouts. Taken by surprise, Alexander I sues for peace. Pledging to an alliance with Napoleon, he is also forced to surrender Lithuania, Estonia, and Latvia to Prussia and Finland to Sweden. Following this, the Duchy of Warsaw led by Stanisław Potocki announced their independence from the King of Saxony. Albert Casimir was crowned Prince of Poland as a figurehead, and Potocki held the real reigns of power. Napoleon immediately ordered Blücher to Poland. With the help of Poniatowski, Blücher led 70,000 Prussians and 50,000 Polish into Warsaw, arresting Potocki and freeing Albert Casimir from house arrest. Albert Casimir was crowned Prince of Poland agaian and recognized by Bernadotte and the Prussian Envoy, Prince Augustus. Posen was given to Prussia for putting down the rebellion.

From here, Napoléon leads France, Italy, Spain, and Austria, reuniting the Western Roman Empire.

Knowing the way Napoleon did things, it'd have been in the form of half-a-dozen states headed by his various siblings, and no way do Jerome and co. accept the feeble and very young Napoleon II as the senior partner in this arrangement when Napoleon finally dies in 1821.