Can I configure the Tor Browser Bundle so that it becomes an extra hop after the Tor exit node without using special OS such as Whonix?
The Tor Browser Bundle just comes pre-configured to use Tor as a socks proxy so as far as I know, you cannot add an extra HTTP proxy after Tor.
Another alternative to using a special OS would be to use proxychains to chain requests through Tor and then an HTTP proxy. You wouldn't necessarily want or need to use the Tor Browser Bundle for this.
I have Tor running locally on port 9050 so I added these lines to my proxychains.conf file under the [ProxyList] section:
[ProxyList]
# tor
socks5 127.0.0.1 9050
# then chain through http proxy
http 2.3.4.5 80
Then to launch your browser which will proxy through Tor and then the HTTP proxy, run proxychains /usr/bin/firefox
It will cause all connections from the browser to first go through Tor, then through the HTTP proxy.
You should see output similar to this on the command line to know its working:
|S-chain|-<>-127.0.0.1:9050-<>-2.3.4.5:80-<><>-74.125.239.39:443-<><>-OK
127.0.0.1:9050 shows it chained through Tor, then 2.3.4.5:80 is the HTTP proxy, and finally out to the destination 74.125.239.39:4443 (Google).
A note on security, I used firefox browser for the example. You could use Tor browser instead but you will want to make sure its proxy configuration is set not to use a proxy since you're already chaining through Tor via proxychains.
Tor Browser will be a little safer since it won't keep history/cache and its signature much less unique.
Hope that helps.