Per Overpacks-Section II, it says: “Individual packages each complying with the requirements of Section II may be placed in an overpack.” This means that individual lithium batteries must be individually packed in an inner packaging and then packed in a rigid strong outer packaging and finally undergo a 12m drop test and must be completed before placing it in an overpack with packages of non-dangerous goods and/or dangerous goods provided none of them will react dangerously with each other. It doesn’t mean that it allows “all packed in one” of Section II batteries and other items. Lithium batteries must be fully completed in compliance with Section II and tested for a 1.2m drop and thence can be placed into an overpack. The other items should not be bare unpacked but must be packed in their individual packagings.
On the other question, the sentence reads: The overpack may also contain packages of dangerous goods or (packages of) goods not subject to these Regulations provided that there are no packages enclosing different substances which might react dangerously with each other. After the word ”or”, the words “ packages of” are abbreviated.
You may overpack a completely done battery package with other packages as long as they do not dangerously react with each other. As you state, an overpack is a packaging done at the discretion of the shipper in desire to assemble several packages into one unit for ease in handling and convenience. A drop test of an overpack is not required.