Hi Lindsay,
I'd recommend limiting the number of categories you select for each post - generally my rule is 3 categories maximum. That being said, I've found that the most successful strategy is to create & categorize content in a way that easily satisfies your user's intent. Categories = broad topics/areas of interest your ideal buyer wants to read about (broad keyword search phrases). Articles/posts = focus on one specific question related to the broad category (longtail phrases).
For example: let's say you have a shoe company and you've created a style blog that discusses the latest trends. One option is to do what a lot of companies do, and choose generic blog categories like trends, inspiration, comfort, etc...
Let's say you research and decide write an article called: Best Shoes To Wear To Coachella (because it's a longtail keyword). How do you categorize it? It's definitely goes in trends, but it's also kind of inspirational, and you also have a section about comfortable shoes to wear to Coachella. You can't choose just one category, so you end up adding the post to 4-5 categories.
The biggest problem with this type of organization structure is not duplicate content - it's that users (a) can't easily find your content because they don't know what your categories mean and (b) they're confused about what content they've already read, because they see the same articles in multiple categories.
In my opinion, the better way to choose categories and article topics, as I sort of mentioned above, is to start with broad topics that people want to learn about.
Instead, you might choose categories based on popular search queries. For example: Festival Shoes, New This Season, Celebrity Favs, How To Wear It, etc. In this case, your article: Best Shoes To Wear To Coachella would go under the festival shoes category. You could also have articles about Stagecoach, SXSW, etc. This isn't the best example, but I hope this make sense!
Long story short: done correctly, this type strategy is helpful in a number of ways: (1) your user is able to easily understand where to find the information they're looking for, (2) you avoid duplicate content, because your articles are written to correspond with 1 (maybe 2) categories, and (3) your category pages will be hyper-optimized for lots of longtail keywords that are related to your main category keyword. This will make your category pages like mini-landing pages that have a higher probability of ranking broad/more competitive keywords.
I hope this helps!