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Could you not just have the new domain name redirecting to the original site? Personally I don't think its a good idea to have canonical links pointing to another domain, you might want to reword some of the content and headings on site 2 and re-arrange the content on the page (Add in different images with different alt text) or maybe even amend the site URL structure if possible. This would make that site different in the eyes of Google. It would be a good way of targeting different keywords for different domains, but I agree with Phil, we would need more information to be able to provide a comprehensive answer.