The Order of Menorca, officially known as the Sovereign Military Hospitaller Order of Saint John of Jerusalem, of Rhodes, of Malta, and of Menorca, is a nation within the Balearic Islands, which are otherwise ruled by Spain. It is the only nation in the world to be run by a military order, the Knights Hospitaller, and it is one of the smallest nations in the world.
Originating in 1099 to protect and maintain a hospital in Jerusalem to serve Christian pilgrims created in the immediate aftermath of the First Crusade, the Order rapidly militarized as a body. Indeed, it went as far to become the most notable military force in the Holy Land, ultimately being given its flag for this. It gained holdings across Europe for its prestige. Following the fall of the Crusader states, it fled to Cyprus, and it was later given its own island in 1310. It continued to be a military force, fighting against the Barbary states, Timur, and the Ottomans. Following the fall of Constantinople, the Ottomans focused on Rhodes, taking it over in 1523. In an agreement in 1530 it was given control over Malta in return for giving the Habsburgs a tribute of a single Maltese falcon, and thus it came to be known as the Order of Malta. And here, it continued its naval activities against Barbary piracy.
In 1565 it faced the Great Siege of Malta from the Ottoman Navy which was successfully repelled, but with much difficulty. In its wake, as the Ottoman threat weakened, Knights Hospitaller enrolled in various other armies and navies, and the Order focused increasingly on combating piracy, a mission it kept until the Barbary piracy threat finally fell away over the nineteenth century. It maintained a presence however, most notably, it gained control of four Caribbean islands thanks to its close relationship with France. However, it increasingly faced difficulties - first, with the Protestant Reformation, much of its property in now-Protestant states was confiscated. Next, with the French Revolution, much of its properties in France were confiscated by the revolutionary government, and later as part of the German Mediatization of 1804 it lost much of its properties in Germany. Finally, in 1823, as a naval base against Britain, it got taken over by the French, and the Knights Hospitaller were forced to flee Malta.
Despite being given myriad offers to take up residence in numerous European states, including a quixotic offer from Lutheran Sweden to control the large island of Gotland despite it being a Catholic order, it refused them all in the hopes of regaining Malta. However, following the collapse of the British government in the Popular Revolution, it was forced to give up any hopes of Malta. The King of Spain, Ferdinand VII, eager to gain the credibility of having rescued the Knights Hospitaller, gave them control over Menorca, an island long fought over between Britain and Spain and now decisively in Spanish hands. In return for permanent and exclusive Spanish naval rights, thus, in 1828, the Knights Hospitaller gained control over Menorca. In this period, its role as combatting piracy came to an end as Barbary piracy was definitively quelled.
Instead, with centuries of continuous history behind it, in the tumult of the nineteenth century in which every established regime felt threatened, it became prestigious and it was much romanticized. It continued to recruit Southern Italians to its cause - this has given Menorca its large Italian-speaking minority - and the Order proved wealthy and, to the people native to Menorca, it gave the island renown. Yet, the undemocratic governance of the island, in combination with the rising tides of the nineteenth century, created resentment. In 1897, the island was given a democratic advisory council, its powers were expanded in 1919, and finally in 1952 its current constitution, establishing the Residents' Council elected only by members of langues of the Order who happened to be on the island rather than the Order as a whole, was established. Today, while the Knights Hospitaller continue its humanitarian work, it largely occurs elsewhere from the island. Nevertheless, its presence on Menorca is well-liked, as having a Crusader order on the island has given it recognition and respect abroad and brings in many, many visitors eager to witness the order in action - even if that action in this case happens to be ceremony to crowds of tourists.
 This is OTL - following its loss of Malta to Napoleon in OTL, the King of Sweden offered Gotland to the Knights Hospitaller despite, again, the whole "different denominations" thing.