Different Shipping Rates for Different Products

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My store is set up for free shipping over $150. However, I have one category of products (Accessories) that I do flat shipping on, and this seems to work fine when customers are only buying products from that product category. However, if someone is doing a transaction where they are buying a product that is eligible for free shipping plus buying an Accessory, I want the shipping to be free. I can't figure out how to set this up because when testing it, it's charging the flat rate even though there are multiple items from different categories and the total is over $100.

Just in case this doesn't make sense:

Non Accessory item < $150 = calculated shipping

Non Accessory item > $150 = free shipping

Accessory item of any value = flat rate shipping

Non Accessory item + Accessory item > $150 = free shipping

Non Accessory item + Accessory item < $150 = calculated shipping


Thanks for any advice!