It depends what type of markup you are adding Melissa. If it's a recipe for example, you'd need to edit each blog post that has the recipe. Most stores will be able to edit their articles.liquid file or similar with the blog structured data.
Without knowing exactly what structured markup you're trying to do, yes, you can edit individual article's HTML content to insert your mark up there. Whether you could do it via a template in your theme is a different question pending what you're trying to accomplish.
Thanks for responding. I'm a Marketer rather than a techie so this is all very new to me.
Basically I have a mix of blogs consisting of recipes, how to guides and news articles. I want to add the appropriate code to each to help them rank and show as rich snippets. When I look at an article in Shopify I can edit the 'content' HTML but I can't access the individual full code for the article. I can get to the code for the template but this is applied to all articles.
Hopefully I'm explaining that OK :)
Am a marketer as well. You have access to the article by editing it so you can add the necessary markup to it. You don't need to edit the theme if you want recipe markup as the markup is done in-line (where the content is). It sounds like you may not have implemented any schema before. I suggest you read up and follow some tutorials. A Google one on recipes: https://developers.google.com/search/docs/data-types/recipe