Or you could just use <blockquote> when you need nested quotes.

Update: To clarify, it doesn't matter if '"""..."""' doesn't work all of the time, since you can fallback to <blockquote>...</blockquote> the rest of the time. And I doubt that anyone has a need to include '"""' in their nodes — a search sample revealed '"""' has only been used in code blocks — so having to use &quote;"" to actually place """ in a node doesn't burden anyone.