Do you know where the monarchies are? Besides the Ottomans, of course.
Norway, Sweden, Denmark, Germany, Poland, Italy, Russia, Vatican, Andorra, Morocco, Turkey/Ottomans, Levant-Hejaz (Ottoman Dominion), United Arabia (Ottoman Dominion with subnational monarchs), UK, Canada, South Africa, Malaysia (British Dominion with subnational monarchs), Papua (British Dominion), Micronesia (BD), Pacifica (BD), Polynesia (BD), Japan, Thailand, Nepal, Bhutan, Brunei and Aceh I am certain of. Algeria might also be an Ottoman Dominion but probably not. I am not certain about Iran, Egypt and Afghanistan (but Iran most likely is while Egypt isn't). I am uncertain of Balkans (Bosnia and Slovakia are republics, Czechia and the rest I am uncertain of). Kamerun and Togo might be German dominions. Portugal is probably a monarchy and Spain probably isn't. Unsure about Cambodia but probably not. Lithuania-Latvia (Baltica) might be a monarchy too.
I must say thank you for asking this. It allowed me to think it over. I will update later, answering uncertainties after I check over the history again tomorrow.
Edit: final decisions: Algeria is an Ottoman Dominion, Czechia and Baltica are monarchies with Romanov cadet branches. Iran and Afghanistan are monarchies while Egypt is a republic. Kamerun and Togo are republics, Portugal is a monarchy while Spain is a republic. Cambodia is a republic. In the Balkans, Greece is a monarchy while others (Romania, Hungary, Bulgaria, Serbia, Albania, Montenegro, Bosnia and Croatia) are republics.