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As Martijn said, tagging multiple categories to a post can help with crawling due to more internal linking. Fortunately, if your URL is just sitename.com/post-title, then you can change/add existing categories and it won't make a difference as the URL won't change, so you won't have to redirect anything. If you're renaming categories, changing the category URLs, you may still want to redirect the old category URLs to the new category URLs to preserve the category pages' authority though. If the site structure is more like sitename.com/category/post-title, that's when it may become an issue and you will want to redirect the old URL to the new URL. If you use Wordpress, I believe it will automatically redirect the old URL to the new URL if you do change the category. (Definitely test this to make sure it works with your version/plugins.) There are also plugins to help you tag multiple categories to a post but, setting a preference for the permalink category.