Several blogs pointing to 1 shop: ok from an SEO standpoint?

I have an online shop I'm trying to build traffic for.
I've decided that I'm going to breakdown the topic into categories and create blogs on new domains with posts and videos so that I can try to rank for longtail KWs in each category.
My question is, can I keep my current shop and have the blogs point to products or categories in my general shop? Or should each new blog have its own shop?
What's best from an SEO standpoint?