The title of the question speaks for it self. Can I configure Tor to use more than three relays (nodes)? I suppose that it won't be possible inside the native Tor Browser, because that can only use three. However, is there maybe another browser, which can connect to the Tor network and use e.g. four relays or more?
You really shouldn't do this: it can deanonymize you and it increases the load on the Tor network. See: https://www.torproject.org/docs/faq.html.en#ChoosePathLength
For a guide on how to modify the amount of hops in the Tor binary, see this guide: https://www.grepular.com/Tor_Circuits_with_Two_Hops_on_Ubuntu
After you've modified the Tor binary, you just need to set the SOCKS proxy port in the
torrc and change your browser's proxy settings to the local SOCKS proxy.