But how would his presidency go then?
He would have a very international policy, doing what he could to increase American influence throughout the America's and Asia based on economic reasoning (in addition to mitigating British influence, largely in the former), and to a smaller extent Africa (of which Madagascar he was particularly interested in, for reasoning I don't readily have access to). Blaine also was a strong proponent for a form of Pan-Americanism, which I imagine would be similar to the OAS as it exists today.
Going by what he sought to do as the Secretary of State from '89-'92, he would push for earlier dominance of the Hawaiian Islands for fear of them falling to the British, if not annexed than as a protectorate of Washington. Blaine was also genuinely interested in the acquisition of Samoa, and may have managed to take it in his entirety, provided he acted with proper haste, though it would harm relations with the British and Germans who also had interests in the area.
Expanding on Blaine's Pan-Americanism, when the International Conference of American States was held in 1890 (the original cancelled in 1881), Blaine was hoping to establish a Custom's Union between the various American States, to construct a Pan-American Railway, and to establish an Organization or process to peacefully deal with issues between the various American States. There were also interests of territorial annexation, but these were not expressed publicly, and were largely limited to Hawaii given Blaine realized that his other two major acquisitions, Puerto Rico and Cuba, were not to be acquired without major diplomatic exertion.
Blaine did still cling on to his Protectionist past however, in ways that benefited the United States; while he was fully supportive of Free Trade with the Americas and other parts of the World, he was wholly against Free Trade with Europe, for fear that it would adversely effect the American economy. I don't have enough knowledge here to dispute that notion, but I suppose it could be true, to an extent.
As for his Domestic Agenda in detail, the closest I could gauge would be what occurred, or what was to occur, in James Garfield's Presidency, given he and Blaine for the most part walked in step together while the two worked in the White House, Blaine essentially serving as his Vizier.
Edit: As an aside, he was also a strong proponent for a Canal through Central America. I believe he favored the Panama option however, contrary to popular political opinion at the time that sought to build a Canal through Nicaragua.
Edit2: And of course, how could I forget; he would pass a number of discriminatory measures against Roman Catholics if he could. Effectively he was a Know-Nothing in that regard, though all his vitrol was almost exclusively directed towards Papists rather than Immigrants.