Asia (Or Eurasia, or Africa/Eurasia) comprise multiple tectonic plates, as does America (or North/South America). Is the area south of the Himalayas a separate continent from the area north because they're on different plates? What continent is Iceland in? Or Japan, much of which is on the North American plate.

There's no clear definition and there's far to much political and cultural meaning in the definition of a continent so any definition involving the term is going to be ambiguous.