So, to actually answer your question:

There is little evidence that the United States ever had imperial ambitions of a traditional, territorial kind (meaning full annexation of territories) that extended to something as vast as a full annexation of all of the Americas. However, the United States has absolutely expanded territorially, politically, and economically to many different parts of the Americas, both in the north and the south. American expansionism has never been limited simply to the West.

The earliest examples of northward expansion were during the American Revolution. The American colonists had hoped that they would be able to rally the Canadian provinces to their side, specifically Quebec. There were a variety of reasons for this: the Americans had a misguided belief that French Canadians would sympathize with their cause, and they mistakenly believed Quebec to be ill-defended. The strategic advantages of Quebec's capture were great, for it would severely hinder Britain's ability to mobilize and move troops against the colonists, especially in New England. The invasion of Quebec by the American colonists was unsuccessful, and Continental troops were expelled from the territory. However, support for Quebec's annexation by the United States persisted well into the 19th century. I'd recommend reading more about the history of the relationship between the US and Canada, because it is very helpful in explaining some of the differences between American and Canadian identity, especially in their relationship to the British.

If we move south, the US definitely annexed many territories. The most significant territorial acquisitions were in the Caribbean: the US annexed most of Spain's colonial holdings after the so-called Spanish-American war in 1898. The US acquired Cuba (established as a "protectorate") and Puerto Rico from Spain. The US also annexed Spain's Pacific holdings in the Philippines and Guam.

There were also significant military interventions and territorial acquisitions in the early 20th century in Nicaragua (1909, full invasion) and in Panama (1904, naval blockade and purchasing of the Panama Canal) that, while not full annexations of those territories, were enormously beneficial to the United States maintaining its geopolitical and economic hegemony in the region. In the previously mentioned cases, the US did not explicitly annex these territories (though the US did control the canal), but the levels of political and economic pressure exerted upon these governments essentially made them puppet states who adhered to US interests.

Which brings me to my final point, which is that expansionism and imperialism don't necessarily have to take on the traditional form of territorial annexation. In fact, most of the history of US imperialism is one of economic, rather than political, imperialism. Part of the reason the US has been able to survive so long as an Imperial power is because it has adapted a far more subtle strategy in maintaining its regional political and economic hegemony. The US may have only intervened militarily in Latin America and the Caribbean in but a few instances, but those actions were crucial in establishing a political base for what later became a strategy of covert support for military dictatorships that supported American economic interests. This was seen in Guatemala, Chile, Argentina and other countries to name a few. I could name a million more examples where the US supported the ouster of regimes it didn't like but I won't bother.

In conclusion, the US has indeed expanded territorially all over the Americas and, where it hasn't, it has opted to maintain more of an economic, rather than political, imperialism. The economic relationship between Latin America and the USA became one of dependency on the US and one can still debate whether that relationship has changed. As far as the fate of some of the US's territorial holdings, that is also mixed: Cuba and the Philippines are no longer in US hands, but there's still Puerto Rico and Guam. As you can see, American imperialism has not only existed on a much grander scale, but it is also extraordinarily complicated to synthesize.