With the wonders of hypertext, it really does not matter where the document is stored, all appropriate pages can link directly to it. I suspect your concern is about the reader in region A who chooses a document in region B, and then ends up with a different template (or at least, different navigation and page headings); no-one wants to confuse their readers.
While there is no duplicate penalty, there is a real risk that only one of the duplicates will be favourably indexed.
The best way, if the site is large, would probably be to use a content management system, that would avoid reader confusion by having any required content appear in the appropriate page. But You'd still have to manage the duplicate URLs with <noindex> or robots.txt to minimise probles - you'd choose which version would be favourable indexed.
Another way, especially for a smaller site, might be to use iframes or server side includes for content.
All these approaches have advantages and disadvantages,and you'll have to decide which will enhance your site more than set limits.
Another way might be to look again at your content, and find another way to categorize it that did not require so much cross-referencing.
Is the regional approach designed for visitor convenience, or structural issues (such as alternative currencies)?
Should you be considering breaking the site into regional sites? - not always useful, as you are then increasing your marketing needs, subdividing your incoming links, and still having potential duplication issues.
The key factor has to be what is least confusing for your visitors.
Your final suggestion sound 'safest', but may need careful attention to navigation, so that visitors can easily get back to the 'region' they came from. A 'back to last page' button may help, if javascript won't hurt.
