I have added both EU and USA eSIMs on the same phone, either thru direct transfer when setting up the new phone, or adding eSIMS via SETTINGS>>CELLULAR>>ADD ESIM
TIM in Italy will not transfer the eSIM directly when setting up. You have to DELETE the eSIM from the old phone and then scan the ORIGINAL QR phone using the ADD ESIM option. When you get an eSIM, TIM tells you to KEEP the origina QR code because you will need it if you transfer the eSIM to a new phone.
In the DR, because of government regulation you HAVE to contact the carrier (no transfer of eSIM allowed when setting up the phone) and they have to verify it is "you". They then issue a new QR code via email and you set it up by scanning the new QR code.