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It's not that the content is duplicated, I don't see the need to use canonical. It's the problem of trying to optimize each language when my branded keywords are the same, and are not only used across the different languages, but also across the different pages of each language. This is because there are certain branded concepts we're ranking for (and trying to rank for). But my concern is the over-use of these keywords and ultimately the different pages and subdomains competing with each other.

Hi, 
What's the best way to avoid different language sub-domains competing with each other in SERPs (en.domainname, dk.domainname etc.) when using the same branded keywords across each domain? The site uses a mix of branded and non-branded keywords, but the branded ones come up A LOT, across many different pages and across all the language subdomains so I'm worried about keyword cannibalization and over-optimization.

Any advice would be much appreciated!

Thanks,