I’m not sure I understand why you think a third interface is needed.
There’s certainly plenty of bandwidth available in the network. Have you given any thought to setting up an additional VLAN on your phone/system interface and using that? Many phones (my experience tends to run to Cisco, but others as well) can use VLANs to sequester traffic logically.
Even if you don’t want to use a VLAN, you can assign multiple addresses to one of your existing interfaces and set up actual networks that way.
Without some information on the topology you are looking for, it’s hard for anyone to give you good information. My gut says that two interfaces may already be one too many, so three would be “right out”.
On the other hand, you can set up as many interfaces as you’d care to. Linux can support over 8 interfaces out of the box, and that’s before you start getting creative with source code changes.