Already in the identification phase mentioned above you should start evaluating the quality of existing knowledge, decision processes and documentation. Focus specifically on EN 13428. Read Chapter 4 in EN 13428 thoroughly. Can be obtained from the national standardization organisations.
You have to render/prove and document that a certain packaging system only uses the necessary packaging volume in order to fulfil its function.
By studying EN 13428 you will realize that the company has a certain flexibility, but consider the fact that the authorities can demand to see your documentation. If you do not reach an agreement you can appeal for judicial settlement. This way the requirements leave room for interpretation and you can meet different interpretations in different countries or regions.