Cant do it through Shopify natively, luckily it shouldnt be too hard to find what your after. You’ll likely need a 3rd party courier. In canada there is a service called netparcel, probably something similar in your neck of the woods. Basically a courier shipping label reseller, usually gives you a nice price break over buying direct from UPS or another company like that. Additional boxes are actually fairly cheap when going through a courier. If im looking at $25 for a single box, usually 3 boxes would be $31ish.
The netparcel app is a free integrate, no fees beyond the normal service prices they charge for the courier label. Good odds something along those lines exists for you.