I dont know if my answer will help, but I have not heard of a program or otherwise that allows you to print multiple labels for one USPS shipment. This is more true for something like UPS - where you can add multiple boxes/packages to one shipment. If you are using smaller boxes, maybe it will help to fit them all together in one that is larger for USPS shipments. USPS has a wide range of box sizes for priority and flat rate shipping, and I believe that you can get them from USPS for free.
I hope this helps in some way.
The app we develop, Advanced Shipping Rules, allows you configure different rates for different groups of products that then get combined intelligently at checkout for your customer.
We also have an advanced feature that lets you specify what package to use based on QTY of items from that group of products.
So you can say
Up to 2 items ship in box size A
Up to 5 items ship in box size B
If someone orders 6 items, we'll rate box B and box A seperately and add them together.
Bob_Burkhart : By default, Shopify packs items in a single box till weight limit of that box is reached. Assigning multiple boxes is not something that is directly feasible. However, you can use the Multi Carrier Shipping label app where you can select Flat rate box for a package. If the weight crosses, the system will automatically use another box to pack the remaining of the items. This way you will have multiple boxes for a single shipment. Was i able to explain this?
Create a shipping only product that sells for $1.00. Each time you need to ship an additional box, go into the product and update the weight to the weight you will be shipping, set your default box to the size of the box you are shipping. You will mark it paid when you add the draft order. You then follow the usual steps to process the order. It's the only way I figured out a way to overcome the issue. Yes, you will have a fee.