I agree with @xenoid. It's not the OS that is concerning, it would be the syntax changes of all the other programs. Essentially copy pasta of what @xenoid said.
If you have two servers you can replicate one domain to the new and
see how it behaves before switching the DNS to the new address. Rinse
and repeat for the other domains. When you'll have done 4-5 domains
migrating the rest should he a snap.
Essentially you would want to mirror your two servers, this will give you the "live environment" and then the server you are moving to.
I would also add, you can just move the actual content to your other server without any issue I.E Photos, music videos web files ETC, since these are going to be unchanged from the distro upgrade. I would also just install a fresh Plesk environment and not worry about copying over the old server.
Once your data is moved over, I would then start building your Apache, Nginx and Bind configuration files, and this is where the fun begins. If you haven't upgraded these servers in a while, the configuration Syntax would have massively changed. I would apply one configuration file, then on my laptop modify my host file to point to the new server, get that one all set, then use that as a template for your other domains.
I typically would script this out. I.E create a list of your domains, then do a for loop
for dom in dom_list.txt; do
cp $COMPLETED_DOM.Config $dom.config
and then Sed change the domain inside the file. (I'm working off 2 hours of sleep)
Once the script runs through, modify your host file on your laptop to test all your domains and bada bing bada booom.