Assuming you want it for job in Asia/ME/Africa, can the local CAA definitely process validation/paperwork conversion with TR NOT on your commercial?
The FAA piggyback does allow adding FAA IR, multi and FAA TRs, but if you get caught out in admin-mess, it'd be of limited use.
OTOH, considering your experience/hours of training, why not go for the FAA commercial/multi IR? IR won't expire, easier to maintain outside Europe, great for N-reg wherever. If you logged some training hours as dual after getting Euro PPL, that can be classified as FAA manipulating controls PIC if you go through records, or whichever requirements. Granted, you'd possibly be looking at 'initial single engine comm' and then adding twin IR privileges after flight test (possibly sim, need to check regs).
Either way, do get everything in writing, your intended training, licence/TRs held and to be held, then see if viable with CAA and prospective employer. Euro airliner TR is different story to FAA's simulator only and if you don't do the sim at EASA approved facility in US, you'd not possibly be able to transfer even that subject to the T&Gs on actual aircraft.