How to select a shipping box for a particular product based on quantity using Drupal Commerce?
Using the Commerce Box module, for which only a DEV version exists, you can create Commerce Box entities, but that's about it. E.g. it does not add any specific Rules Actions you can use to select the appropriate shipping box, such as based on product items and/or quantities.

However, there is an inspiring issue for the Commerce Fedex module, titled "Allow altering of default package dimensions". And comment nr 17 of that issue contains an interesting patch which allows for package dimensions alterations.