In our TL, before the U.S. closed its doors to them in 1882, we had large numbers of Chinese immigrate to the United States in the 19th century. In addition to this, we also had some immigration from the Ottoman Empire to the U.S. in the late 19th and early 20th centuries. (Also, large numbers of East Asians immigrated to Hawaii--which became a part of the U.S. in 1898--in the late 19th and early 20th century.)
Anyway, what I am curious about is this--are there any additional Third World countries or colonies from which the U.S. could have realistically experienced large-scale immigration in the 19th and/or early 20th centuries? Also, if so, exactly which countries are you thinking of here?
Any thoughts on this?