Shipping cost for multiple items

[titan12]

Some of our products use different package sizes. However, if two or more item is ordered the package size may change. How do I get it to update cost?
Example:
Pirate ship shows for 3 items same item 12x6x6 box $12.43
Shopify shows $9.20
The cost should be closer to $12.43 but, I can't get close to each other.

I do have different shipping profiles already set up since some products can only ship ground. And all items have the correct total weight including, packaging.

[ShipAntdotcom]

It is very hard to estimate multiple items weight and volume especially irregular products. Thus I suggest you get the weight and volume respectively for each product from supplier, then calculate shipping respectively when there are multiple items in one order, of course, you can offer some discount.