Commenting on old Chain Proxy Request Apps posting by Ross Goodman
In my search for a proxy that would allow modification of headers, I came across https://portableapps.com/node/777 page. Then, after finding and starting to use proxomitron, I remembered the aforementioned person's issue, and realised that this program also solved his issue (At least I think I understand his issue - http://www.inetprivacy.com/a4proxy/chaining-proxomitron.htm).