Are multiple hyphenations allowed in extending compound words like "well-controlled"? [duplicate]
Solution 1:
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.
Solution 2:
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".
Solution 3:
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.
Solution 4:
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.