The UAE is a federation of seven emirates, which are by themselves monarchies. The president of the UAE is by convention emir of Abu Dhabi, and the prime minister is by convention the emir of Dubai.
Andorra has two co-heads of state: the Roman Catholic bishop of Urgell and the President of France. One is appointed by another head of state, while the other is elected by the people of a foreign country.
Andorra calls itself a principality, which means that technically, arguably, it would be a monarchy. Although, I agree, de facto it is somewhere between monarchy and republic.
Also add the Vatican, which is somewhat unique
