Which nations could've plausibly undergone rapid modernization, as Japan did?

I would say an post-independence Argentina-Uruguay without 50 years of civil war between Unitarians and Federalists and Argentina-Uruguay had constitutional monarchy as Belgrano intended. An earlier stabilized Argentina-Uruguay would have become a serious economic competitor of the United States and competitor of recruitment of immigrants thus Argentina-Uruguay ATL might have a larger Irish and German than Italian and Spanish in OTL.
 
I would say an post-independence Argentina-Uruguay without 50 years of civil war between Unitarians and Federalists and Argentina-Uruguay had constitutional monarchy as Belgrano intended. An earlier stabilized Argentina-Uruguay would have become a serious economic competitor of the United States and competitor of recruitment of immigrants thus Argentina-Uruguay ATL might have a larger Irish and German than Italian and Spanish in OTL.

I'm sorry, but Argentina is not going to have a monarchy. Buenos Aires was basically rebel territory since day 1, when they finally shake off the Spanish monarchy the people aren't going to tolerate another one.
 
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