Networks are supposed to do egress filtering to prevent any packets with fake IPs from ever leaving the network. In practice it's not always so, but it mostly is. So you'd be limited to fake IP addresses in your own network, and doing so might raise alerts depending on the network infrastructure you live in.

Packets with fake source address can easily be spotted, and will raise an alert. In terms of using multiple interfaces for a single service it might be easy to hack together in a python script, but last time I checked the linux kernel support for bundling multiple interfaces is limited to redundancy and failover.

What I'd like to have is a single service dynamically using many network interfaces with randomized packet timings and randomized packet scheduling (5 packets on first interface, pause on 2nd, some on third interface, sometimes send traffic simultaneously).