Edit - based on comment that I should do better to explain.
If you want to isolate the servers' communication on the cable, disregarding any services you may use, VLANs is one of the options. VLAN (virtual LAN) is a way which isolates the computer at data link layer alias for OSI model layer 2. You will have to change your firewall and routing to accommodate the changes.
On the Windows level you need to enable tagging on the NIC (go to the NIC properties and you should select an option named VLAN). On the switch you need to addadd multiple VLANs to the port the NIC is connected to and the tagging will determine which VLAN the traffic goes to.
If you have cisco you can add (I prefer this one as it is non-destructive) it (e.g. VLAN 10):
switchport trunk allowed vlan Add vlan10
or you can overwrite your current VLAN config with:
switchport trunk allowed vlan 10,20,30,90
Vlan vs. subnets - VLANs work on OSI layer 2 (data) and subnets on OSI layer 3 (network) - Vlan or Subnet.
Edit for the comment:
@Cory Knutson - Are you saying to create vlans with /29 subnets, and
have the backup server have an IP in each?
Depends on how many servers can be at one VLAN if only one he could have /30 - 2 hosts (that would have only backup server and the server itself -> not that practical). If he wants more, which is unknown, he may want to have /29 for 6 hosts; /28 for 14 hosts etc. you know how to do the subnet calculation.