If you are using DirectAdmin for your server it actually very easy.
Since version 1.36 there is a BETA feature where you can Add an Ip to you domain. Previous it was only possible to add a domain to a user/reseller.
SO how does it work. You have a working wordpress network with subdomains and the domain mapping plugin installed:
on your server using DirectAdmin
1. Add an Ip to Direct admin. | Admin Tools > "IP Management" in Admin mode
2. Asign the Ip to Admin
3. go to "Modify User". Show all users> click user> click button modify user.
4. Add Additional IP. Choose the new IP and click the add button.
5. login as the User.
6.got to "Domain Setup" click on the domain you want a second IP for. (The domain you have installed WordPress on). At the bottom, "Add Another IP to yourwordpressdomain.com"
Ok thats for the server settings.
1.In the domain mapping plugin settings you need to use the CNAME option. Server CNAME domain: (yourwordpressdomain.com). Or else it won't work.
2.create a Site (something.yourwordpressdomain.com)
3.Map a new domain to it:
http://www.newdomain.com (primary) and newdomain.com (without the www and not primary) to the something.yourwordpressdomain.com ID
Now go you the DNS settings of your newdomain.com
1.Add 2 A records:
http://www.newdomain.com A 18.104.22.168 (the added second IP in Directadmin)
www A 123.1123.123.1 (the added second IP in Directadmin)
Thats it. you now have 2 domain names with different Ip adresses pointing to a single wordpress installation.
Just wait until everything resolves. It can take some time.
....and to finish the discussion why it has no added value using multiple IP's. It has no value. if you doing it for SEO google will find out.
To make it actually Google proof you should probably also have different nameservers and ICANN registration names.
Having multiple nameservers for a single wordpress multisite.
It will cost you many IP adresses. Consider if its worth even trying.