I have posted https://serverfault.com/questions/823389/how-to-route-traffic-between-my-nics-on-linux-which-connected-to-proxy-server?noredirect=1#comment1049296_823389 and got marked as "on hold" because it is believed that it is off topic.
I believe this is a legitimate question as I believe there must be a way to do forwarding through some sort of ssh port forwarding or playing with the routing rules etc. I do not believe this is something IT should care because all the traffic will come from my account through the web proxy anyways.
Can we please discuss if my question is really off topic or not?