Our shipping calculation settings are explained on this help page:
Our USPS rate lookups only obtain general Package rates for the order weight, number of separate parcels, and origin/destination ZIP codes. Our system can only handle a common origin ZIP code for all products in a given seller's account, so this approach may not work well for you with products being shipped from different origins.
I might suggest using product-specific flat rates per unit and/or the Cost settings for various Packaging Types to handle flat rates per different types of product -- e.g., you could do something like 6 bags of beans fit in a Small Box, shipped at $1 per bag plus $4 for the box (i.e., $5 for the first bag plus $1 for ea. add'l bag up to 6), so 7-12 bags would kick in another $4, etc. Different products could have their own per-unit rates and use a different Packaging Type with its own Cost. If you'd rather have the same baseline cost (first-item surcharge) regardless of the products ordered, that could be done most easily with a flat Handling charge rather than using the Cost settings on Packaging Types.