How you should hyphenate depends on your publisher. For example, at O’Reilly Media, their style guide explicitly directs you not to use a hyphen with four prefixes:
- Unless part of a proper noun, close up words with the prefixes “multi,” “pseudo,” “non,” and “sub” (e.g., “multiusers,” “pseudoattribute,” “nonprogammer,” and “subprocess”).
However, the word pseudo-tty is specifically grandfathered in under that spelling because of its historical use that way in Unix operating system technical documentation.
For the most part, hyphens are best used for temporary, impromptu compounds, not for established words, where their repetition just looks messy. North American publishers are distinctly less hyphenated than British publishers. Here’s an exercise that draws attention to these differences.
Remember, the goal is clarity. Even American publishers may ocassionally retain the hyphen when the prefix is applied to a word that starts with the same letter as the prefix ended with:
- a non-native solution instead of a nonnative solution
- post-traumatic instad of posttraumatic
- circum-meridional instead of circummeridional (but circum-Mediterranean has a capital, so its hyphen should be retained)
- a re-election campaign instead of a reelection campaign
- co-ownership instead of coownership
During an earlier era than our own, but not so long ago as not to be seen, adjacent vowels in hiatus were marked with diaeresis instead of a hyphen:
- a reëlection campaign
However, apart from The New Yorker Magazine, such careful typography is today seldom seen, and the the tyranny of typewriter’s impoverished character set is widespread: if people don’t have a key with a character on it, they probably won’t use it, even when it would be much better if they did.
Additionally, metric prefixes are never hyphenated, so it is always a milliampere not a milli-ampere.
So with clarity in mind, with a proper noun that is an open (read, unhyphenated) compound, you should have no trouble applying the prefix just the first word:
However, with a multiword phrase — and do notice I did not say a multi-word phrase — in which nothing is capitalized, this becomes ambiguous in standard written English, because you do not know whether the prefix is intended to distribute across the whole phrase. If you write:
Are you talking about nonsalt as well as about pepper, or are you talking about something which is neither of those?
One solution is to hyphenate the whole phrase and then apply an en dash for the prefix:
- a salt-and-pepper look versus a non–salt-and-pepper look
You might try an en dash on open compounds, too, where it works better than a hyphen:
- a salt and pepper look versus a non–salt and pepper look
But you should be careful with that, because multiword adjectives are typically hyphenated.
For a recent book of my own on computer programming, I wound up using a distinctly programmer-friendly invention. I put parentheses around the open compound and applied the prefix to the whole thing. So instead of writing either of:
I instead wrote:
- The difference between a word boundary and a non-(word boundary) is. . . .
It worked well for that audience, meaning programmers. But whether you care to be so bold in general English is something you should think about carefully.
Remember, clarity is the goal.