If you are running Linux you can use program like Proxychains. It allows you to specify a sequence of proxy servers which will be used to run traffic. As first server you should specify your existing proxy server. As second server you should specify any proxy server which you want (if your existing proxy allows connection to them).
It will look like that:
You computer -> (port80)(corporate proxy) -> (port443)(another proxy) -> (any port)(requested resource)
Everything depends on what are the access policies on proxy servers which you will use.
Your corporate server most likely will allow you to establish connection to port 80 or 443 of external computers in the Internet. If you will find open proxy server which accepts connection on ports 443 or 80 then you can route your traffic thru it as shown above. On first look it will not be suspicious because in corporate server logs it will appear as connection of type CONNECT to the external host. Usual web surfing. But in actuality it can be any traffic.