Shopify doesn’t allow you to set shipping rates per quantity out of the box. It can only be based on item weight or order price. For “per quantity” shipping rates consider using apps such as Calcurates. Its Table Rates feature has an FPI (fixed per item) calculation algorithm and you can apply different rates for specific quantity tiers.
@emjayp I recommend charging flat rates based on weight instead of the quantity of products in the cart. This will give a much more realistic estimate of shipping cost and prevent shipping costs from going too high for bulk buyers. Weight-based shipping can be configured within Shopify natively. You can check out the Shopify shipping guide here: https://help.shopify.com/en/manual/fulfillment/setup/shipping-rates/understanding-shipping-rates
However, if you still wish to charge shipping per quantity or based on the packaged boxes, I recommend using carrier-calculated shipping rates for accurate estimates. You can set up precise shipping rates per quantity and the packaging boxes using our Multi-Carrier shipping label application for Shopify. This way you will be able to charge accurate shipping costs and will also be able to buy postage with your preferred shipping carrier within Shopify.