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So apart from Trump and Truman, what are the other possibilities--both before and after 1900?
The most obvious is Lyman Trumbull, who might have been the Republican candidate for POTUS in 1860 if his fellow-Illinoisan Lincoln had not been available. He also could have been the Liberal Republican candidate in 1872 (though he would probably have lost to Grant). https://en.wikipedia.org/wiki/Lyman_Trumbull