In OTL most of Patagonia was in native hands until the Argentine "war of the desert" of the 1870s or 1880s.
Could this have provided an opportunity for a European state to colonize the land.
From the late 1700s through the middle 19th century, Britain seems to be the power with the most raw strength & disposable resources to throw at a Patagonia project. France strikes me as the other, second place, contender. I don't see Spain as having the ability to succeed in both defeat the natives and hold off Argentine and Chilean attacks to set Patagonia up as a sort of "Canada" for loyalist refugees.
The British, perhaps could take Patagonia as a consolation prize for failing to conquer Buenos Aires, or they could decide on that rather than Australia as the location of their penal colony?
In a later era, perhaps a British Patagonia could be a vanity project of Palmerston when he is not too busy with the Crimean War, Arrow War and Sepoy mutiny.
Or Patagonia could become a vanity project for Louis Napoleon, one that might even last, if the situation in Mexico is not so conducive to an intervention in the 1860s.The circumstances of the Paraguay war may lend themselves to this, if France were to ally with Paraguay for instance and keep Argentina and Brazil too busy tto protect Uruguay.
Another alternative, that would yield better quality land, but also a larger alien population, would be a takeover of Uruguay. Argentina/LaPlata may have been too much for the British to bite off in OTL, but Uruguay seems more manageable an area to pacify.
Either the British under Palmerston or French under Louis Napoleon, if motivated to do so, could occupy Uruguay from one end to the other.
Now I don't think Patagonia nor Uruguay could be made tempting for Maximilian.
Thoughts?