Mdtryhht

I'm confused about how to combine an open-form compound word with a word that would normally be hyphenated. There's excellent guidance for making the open vs. closed vs. hyphenated decision, but I don't see how to apply this when hyphenating the open-form word looks wrong.

For example, make a compound word out of North, America, and based. North America is open formed and something-based is hyphenated. Is Coca-Cola a...

North America-based company: this seems very wrong as it de-emphasizes North America as a proper-noun place and makes it sound like the company is based in the North part of America (which is neither accurate nor the intent of the phrase).

North America based company: feels jolting to read and omits what seems like a necessary hyphen before "based"

North-America-based company: looks best(?), but has hyphenated the open-formed compound "North America", which unlike "well-thought-out plan" still seems wrong, despite the guidance at the linked answer above regarding phrasal adjectives*.

_{* the aforelinked answer says every word is hyphenated in phrasal adjectives , but for some open-form words this looks wrong}

Note: I think my question could be improved with an example that looks even more egregious, but I can't think of one.

The Chicago Manual prefers a spare hyphenation style; their guideline is "hyphenate only if doing so will aid readability". So Chicago would recommend North America based.

When I look up based in Wordnik, all of their examples where based is preceded by a proper name use the hyphen, e.g., U.S.-based, N.Y.-based, and so North America-based by extension.

However, I would share your reservations about joining America to based, and would use North America based.

The Chicago Manual notes:

Far and away the most common spelling questions for writers and
editors concern compound terms—whether to spell as two words,
hyphenate, or close up as a single word.

To aid your decision, they offer this handy table.

One thing some style manuals suggest in this case is to use an en-dash rather than a hyphen. So

North America–based company

rather than

North America-based company.

The longer dash signals that it shouldn't be parsed as "America-based".

Based on a cursory scan of Google Books for North America based, where their search engine ignores any punctuation marks between the words, I would guess that about 2/3rds of all relevant instances were North America-based. But I see nothing wrong with omitting the hyphen.

I didn't see a single instance of OP's doubly-hyphenated version, which looks decidely odd to me.

Rewrite the sentence to avoid the problem:
Coca-Cola, based in North America, makes sugared water.
Coca-Cola, headquartered in North America, makes sugary water.

Or just drop "based"
North America's Coca-Cola makes sugar-water.

My convention is that I hyphenate if the term modifies the following noun, so "North American-based company" is correct.

My related convention is that if the modified noun precedes the -based language, I remove the hyphen: "the company is North American based." This is consistent with the Chicago Manual recommendations.

When a noun is preceded by many adjectives, they are adjected to it
right to left, beginning with the closest.

.. [c [b [a n]]] ..

Thus, an unnecessary fluff remover is an unnecessary remover of fluff.
The structure of this phrase is

b [a n]

If one wants to refer to a remover of unnecessary fluff, one cannot do
this by bringing about the structure

[b a] n

There is no way of doing this. The only possible solution is to combine
the two adjectives into one. This is done using a symbol whose name is
literally under one (ὑπ' ἕν), namely the hyphen. Thus, the structure
of unnecessary-fluff remover is

a n

The only way to turn an expression consisting of many words into a
single attribute is to substitute hyphens for its spaces.
Whence:

North-America-based company

This may seem unsatisfactory on account of the fact that North and
America are more tightly connected than America and based. To
address this concern, we might introduce a weakened hyphen and represent
it by the en-rule (--), whence:

North-America--based company

The weak hyphen has a larger scope, allowing it to connect standardly
hyphenated expressions as well as single words.

The problem with the suggestion from @PeterShor is that in

North America--based company

North and America are not connected at all, and there is no need for
the weakened hyphen, since there is nothing relative to which it is
weaker. Nor is any hyphen able to reach across a space. If he meant
something different, it is not apparent from his answer what magical
powers his en-rule possesses that it may connect three words using only
one connector. As far as I can see, his solution refers to an
America-based company that is North, just as

North America-based company

does. The idea of hyphens of different powers is, to my knowledge, from
Fowler in A Dictionary of Modern English Usage (p. 244, ''[o]bviously
connexions of different power are needed''), his example being

the Lloyd-George--Winston-Churchill government

or

the Lloyd-George=Winston-Churchill government

Fowler notes that ''this is an innovation that would hardly find
acceptance.'' But also holds that it is the only logical way of using
these words in this order and sense. It is clearer in his example that
hyphens of only one power are unsatisfactory. In our case,
North-America-based company seems as acceptable as well-tought-out
plan (the alternative being well--thought-out plan).