@firephil
The best way to achieve this is the migration manager in Plesk, that can be found under "Server Management", "Tools & Settings".
The main advantage is that you can use a clean installation of Plesk on each new server and, afterwards, migrate domains, content thereof, settings etc.
Note that it is adviceable to migrate domains on domain-per-domain basis and/or restrict the number of domains to a limited set per migration (and migrate license keys(s) and the server settings
after all domains, resellers, clients etc. are transferred succesfully).
The above method allows for a graceful migration, with a possibility to adjust DNS seamlessly (note that DNS changes, pointing to the new server, can take a lot of time before they become visible in the whole internet, so migrate data and content first and change DNS over the weekend or any other period of low traffic, by preference at night).
Also note that it is very adviceable to
make backups before migration.
And finally, plan some time for the whole migration, if the migration concerns a lot of data: the migration process can be relatively slow (amongst others depending on the available bandwidth). If the migration process becomes too slow, you can also copy the backups to the new server and restore them on the new server, in order to mimick the migration process (this also can take a considerate amount of time: it is faster than using the migration manager, but also more error prone).
Naturally, you can combine the two processes (using the migration manager AND the backup-restore-on-new-server process) and execute both tasks simultaneously, in order to increase migration speed.
Hope the above helps...
Kind regards...