[I just wrote]: The expression "you may/might (just) as well + infinitive" can be used sarcastically and emphatically to introduce a more exaggerated, extreme example than the already quite surprising idea mentioned in the preceding sentence.
In the case of a more-than-two-word compound adjective, the choice of whether to link some part of it with a hyphen(s) or not does not always come easily…
Best Answer
"The already quite surprising idea" actually isn't a compound adjective; it's a noun phrase, headed by the noun idea, and is parsed as "the [[already [quite surprising]] idea]".
However, "already quite surprising" is a multiword adjective phrase used attributively before a noun, so it's possible to hyphenate it; we can write "the already-quite-surprising idea". I don't recommend that, though; already and quite are both recognizably adverbs, so the hyphens aren't needed for clarity, and would be unnecessarily informal. (Not that there's anything wrong with being informal; but "the already quite surprising idea" is not the sort of thing you'd say if that's what you were going for!)