There was certainly interest among groups of people and politicians across American society that thought that ‘Manifest Destiny’ should apply towards the northern territory of Canada (even before the idea of Manifest Destiny was coined by Sullivan). John Quincy Adams ones wrote that:

“The whole Continent of North-America appears to me destined by Divine Providence to be people by one Nation—speaking one language—professing one general system of religious and political principles and accustomed to one general tenor of social usages and customs—For the Common happiness of them all, for their Peace and Prosperity, I believe it indispensable that they should be associated in one federal Union—The relative proportion of power between the different members of this Union.”

This idea of continentalism (in which the United States was to encompass the entirety of the North American continent) was not just Adams’ belief. Various forms of ‘filibusters’ existed during the 19th century of United States expansionism. The idea also likely extends further, given that the entire area of what is modern-day Michigan and everything north and west was also under British control (just not as populated as the coastal parts of the original 13 colonies and… the Quebec Act). The Napoleonic wars during the 1810s also fueled this idea. Leftover resentment from the Civil War even impacted interactions post 1865 (some Confederate forces raided Vermont from British controlled land)! US politicians also wanted to continuously distance themselves from the ‘old world’ of European wars that seemed to never end (this extends forward in history to both World Wars, even). Given the recently earned independence that the colonists fought for, it makes sense that the United States would want to continue the expulsion of European influence from the continent. But the War of 1812 (viewed by some as an extension of the Napoleonic War and viewed by others as continued US pressure against British influence) largely ended in a stalemate with the borders separating the US and British controlled Canada remaining the same. This excludes a later treaty within the Oregon Territories that would peacefully divide the region between US expansion and continued British control north of what is modern-day Washington state.

Back to the filibusters… Filibusters were individuals that normally operated outside of approval from the United States government in order to take over sovereign nations (that were often weak due to political strife) for their own gain. William Walker, a filibuster from Tennessee, is probably the most well-known. Walker took over much of Nicaragua with his private army in order to expand his economic prospects in the region. Filibusterism can absolutely be viewed as an extension of Manifest Destiny, though, and was usually done under the context of creating governments that were more friendly towards American business interests/that could be exploited for business interests. Following the idea that fueled the Monroe Doctrine, many politicians wanted to expel British influence from the continent. Similar ambitions were used in the northern territories as well, but not to the same extent. A good example would be The Fenian Raids in which Irish-Americans and Irish fighters attempted to invade parts of the British controlled Canada in order to expel them from the continent. This was essentially a continuation of the war between Britons and Irish on the main island in Europe. Essentially, though, Canadian history painted a different picture. Sure, there was interest in gaining control of the northern lands, but due to the war of 1812 and the loyalties of people living in the region, they never joined the American rebellion the secured the freedom of the 13 colonies. Instead, the people of Canada forged their own paths and eventually secured their own freedoms as America continued to interest itself in western/southern lands and expeditions.

Sources
Power, Michael. The Canadian Journal of Irish Studies 18, no. 1 (1992): 224-26. Accessed July 10, 2020. doi:10.2307/25512917.

Frymer, Paul. "The Limits of Manifest Destiny." In Building an American Empire: The Era of Territorial and Political Expansion, 172-219. PRINCETON; OXFORD: Princeton University Press, 2017. Accessed July 10, 2020. doi:10.2307/j.ctt1vxm7rr.9.

Sharp, Paul F. "Manifest Destiny Looks North." In Whoop-up Country: The Canadian-American West, 1865-1885, 292-312. University of Minnesota Press, 1955. Accessed July 10, 2020. www.jstor.org/stable/10.5749/j.ctttt6b8.18.

May, Robert E. "Young American Males and Filibustering in the Age of Manifest Destiny: The United States Army as a Cultural Mirror." The Journal of American History 78, no. 3 (1991): 857-86. Accessed July 10, 2020. doi:10.2307/2078794.