We grabbed Texas, California, and everything in between from the Mexicans? Why not some stuff in the Caribbean? From American Ulysses: A Life of Ulysses S. Grant:
Babcock returned in September and presented his findings to a flummoxed Fish. Babcock left with no diplomatic powers but returned with a draft for annexation. The United States could either purchase Samaná Bay for $2 million or annex the totality of Santo Domingo [present-day Dominican Republic] by becoming responsible for its public debt of $1.5 million. The protocol also stated that President Grant would use “all his influence” with Congress to accept a treaty. Grant agreed to Babcock’s draft and asked Fish to write up a formal treaty.
See the Wikipedia article on the Annexation of Santo Domingo, which I’d completely forgotten (if indeed I had ever been taught about it). Part of the idea was that former slaves would want to move to this new U.S. territory. As crazy as this may sound today it was apparently seriously considered.
We were also involved with Cuba:
Even as Grant appointed John Motley minister to the Court of St. James to help deal with a long-term relationship across the Atlantic, a crisis in the Caribbean demanded the president’s immediate attention. Only four days after his inauguration, reports trickled in of a clash between four thousand insurgents and fifteen hundred Spanish soldiers on Cuba, the Caribbean’s largest island, situated just ninety miles from the United States.
But starting in the 1850s, Cuban merchants and planters demanded economic and social reforms, climaxing in an October 1868 uprising that proclaimed an independent Cuba. Spain, in a weakened condition both politically and economically, struggled to respond. Americans responded. Instinctively, they supported what they saw as Cuba’s courageous struggle to chart its own destiny. Veterans of the Civil War, both Union and Confederate, proclaimed themselves ready to support Cuban patriots. The New York Tribune and New York Herald sent correspondents to cover the revolution, reporting that more than half a million African slaves still toiled on Cuban plantations five years after the United States had emancipated its slaves. In April 1869, the insurgents adopted a constitution abolishing slavery.
More: read American Ulysses: A Life of Ulysses S. Grant