I posed this question at the recent EASA Combined Aircrew TeB / FS.TEC meeting. The answer was YES - all valid licence ratings and certificates gained in one Member State shall be included in the new licence following State of Licence Issue transfer. Mutual recognition and no loss of privileges on transfer are embedded in EU law.
The IAA has been particularly at fault over this. They have even refused to accept CRI Aerobatic Instructional privileges from another MS, because "It wasn't their policy". Also FE certificates have been refused after SOLI transfer, because "We have enough of our own". Such restrictions are, in fact, contrary to EU law.
Switzerland might be a bit more awkward as it is a non-EU EASA MS.
One exception is the IR(R), whether using the privileges, instructing or examining. As the IR(R) may only be included in UK-issued Part-FCL licences, no other MS can include it in any licence they issue on transfer. So someone instructing at a UK ATO with a Danish-issued licence cannot provide IR(R) instruction.