---- but have not found an answer to my original question,
Risk,
With respect, you have been answered, there is no ICAO mechanism for transferring an MPL across borders, and no intended mechanism to transfer an MPL between airlines.
The intent of the MPL is, I would have thought, abundantly clear, it is tied to a particular carrier.
The MPL does step up to an ALTP/ATPL once you have all the hours requirements ---- all of which are gained either during the initial course or during time as a co-pilot-F/O.
Otherwise, you will need to negotiate with whatever NAA you are dealing with, as to what credits you will get against the requirements for a CPL, and what additional training and/or examinations that may be required.
Tootle pip!!
PS: That a variation to this was negotiated by one of the Scandinavian NAAs was a somewhat special case, but an example of how an NAA can be sensible and pragmatic. I wouldn't expect that as a general precedent.