Alright my plans for the evening got cancelled so I decided to have a go at working this out. Methodology, a term I am using somewhat loosely, was to go down wikipedia's list of largest empires, ignore each one that was already completely covered (the four big caliphates and several Chinese dynasties in particular), then take their peak territory from Geacron. Geacron isn't an ideal source here, not least because the only way to "export" from it without paying money is print screen, but it's good enough for these purposes. I also didn't bother filling in the entire map because a couple of places were basically just going to come down to whichever country had them today due to how difficult to conquer they have historically been. Priority in overlaps is given to the larger empire. The result is this: https://i.imgur.com/kLNjpSm.png

On here we have:

• Britain in 1920 (including dominions)
• Mongolia in 1259
• The USSR in 1945
• Russia in 1895... basically only because of Finland and Latvia
• Qing dynasty in 1790
• Spain in 1810
• France in 1920
• The Abbasid caliphate in 750
• The USA in 2022. We could have used 1946 to get part of Germany, but we needed Germany in here anyway since the British and Soviet areas aren't included due to different territorial peaks.
• Brazil in 1889
• Japan in 1942
• Rome in 117
• Portugal in 1894 (mainland Portugal is already covered by Rome, though)
• Italy in 1941 (mainland Italy is, of course, also Rome)
• Belgium in 1939 (Rome has the core again)
• Netherlands in 1938
• Denmark in 1917
• Germany in 1941

This list leaves Western Sahara, Liberia, Sweden, Slovakia, Nepal, Bhutan, Papua New Guinea, and Antarctica for a total of 25 countries (or maybe 27 if you add Norway and Chile for maximum Antarctic coverage. I suppose you could also argue that the Treaty of Torsedillas granted half of Antarctica each to Spain and Portugal, not that either ever actually controlled it). Possibly also some islands, especially in the Pacific, but the map isn't in a high enough resolution to tell. The most contested areas are the Levant and Central Asia. Some big empires that aren't on the list include every Persian empire, the Ottomans, and Alexander's empire.