I run a full Bitcoin node on a powerful server however rather than setting up multiple I was wondering if it's possible to use multiple IP addresses on one installation and one running process? Without people being able to detect it's the same node (not easily anyway).
If you can allocate multiple IP addresses to one machine (hint: you can), then yes, you can have one node bound to multiple IP addresses and serving peers on all of them. It's impossible to tell whether two nodes you are connected to are actually the same node so that doesn't matter. Note that doing this does not help the network any more than having one IP address and one node.