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If you're canonicalizing duplicate pages to a single source, assuming it's the one you want to promote, then no, it shouldn't hurt your SEO. The site you're pointing at should see some benefit, and the ones doing the pointing will take a backseat, possibly drop a bit. I'm guessing that's the whole idea? But why do you have multiple sites that have the same products and descriptions if you're not trying to drive organic traffic to all of them? Is it more for paid landing page purposes? If not, why not 301 them to the main site instead? Or, as EGOL suggested, build out content that makes each site uniquely helpful and authoritative so that those canonicals aren't necessary?